annotate doc/manual.tex @ 1515:8c65218920cf

Stop using -fno-inline by default
author Adam Chlipala <adam@chlipala.net>
date Sat, 23 Jul 2011 09:42:34 -0400
parents dbb461e55eda
children c4f39b49aa2d
rev   line source
adamc@524 1 \documentclass{article}
adamc@554 2 \usepackage{fullpage,amsmath,amssymb,proof,url}
adamc@524 3
adamc@524 4 \newcommand{\cd}[1]{\texttt{#1}}
adamc@524 5 \newcommand{\mt}[1]{\mathsf{#1}}
adamc@524 6
adamc@524 7 \newcommand{\rc}{+ \hspace{-.075in} + \;}
adamc@527 8 \newcommand{\rcut}{\; \texttt{--} \;}
adamc@527 9 \newcommand{\rcutM}{\; \texttt{---} \;}
adamc@524 10
adamc@524 11 \begin{document}
adamc@524 12
adamc@524 13 \title{The Ur/Web Manual}
adamc@524 14 \author{Adam Chlipala}
adamc@524 15
adamc@524 16 \maketitle
adamc@524 17
adamc@540 18 \tableofcontents
adamc@540 19
adamc@554 20
adamc@554 21 \section{Introduction}
adamc@554 22
adamc@1160 23 \emph{Ur} is a programming language designed to introduce richer type system features into functional programming in the tradition of ML and Haskell. Ur is functional, pure, statically-typed, and strict. Ur supports a powerful kind of \emph{metaprogramming} based on \emph{type-level computation with type-level records}.
adamc@554 24
adamc@554 25 \emph{Ur/Web} is Ur plus a special standard library and associated rules for parsing and optimization. Ur/Web supports construction of dynamic web applications backed by SQL databases. The signature of the standard library is such that well-typed Ur/Web programs ``don't go wrong'' in a very broad sense. Not only do they not crash during particular page generations, but they also may not:
adamc@554 26
adamc@554 27 \begin{itemize}
adamc@554 28 \item Suffer from any kinds of code-injection attacks
adamc@554 29 \item Return invalid HTML
adamc@554 30 \item Contain dead intra-application links
adamc@554 31 \item Have mismatches between HTML forms and the fields expected by their handlers
adamc@652 32 \item Include client-side code that makes incorrect assumptions about the ``AJAX''-style services that the remote web server provides
adamc@554 33 \item Attempt invalid SQL queries
adamc@652 34 \item Use improper marshaling or unmarshaling in communication with SQL databases or between browsers and web servers
adamc@554 35 \end{itemize}
adamc@554 36
adamc@554 37 This type safety is just the foundation of the Ur/Web methodology. It is also possible to use metaprogramming to build significant application pieces by analysis of type structure. For instance, the demo includes an ML-style functor for building an admin interface for an arbitrary SQL table. The type system guarantees that the admin interface sub-application that comes out will always be free of the above-listed bugs, no matter which well-typed table description is given as input.
adamc@554 38
adamc@652 39 The Ur/Web compiler also produces very efficient object code that does not use garbage collection. These compiled programs will often be even more efficient than what most programmers would bother to write in C. The compiler also generates JavaScript versions of client-side code, with no need to write those parts of applications in a different language.
adamc@554 40
adamc@554 41 \medskip
adamc@554 42
adamc@554 43 The official web site for Ur is:
adamc@554 44 \begin{center}
adamc@554 45 \url{http://www.impredicative.com/ur/}
adamc@554 46 \end{center}
adamc@554 47
adamc@555 48
adamc@555 49 \section{Installation}
adamc@555 50
adamc@555 51 If you are lucky, then the following standard command sequence will suffice for installation, in a directory to which you have unpacked the latest distribution tarball.
adamc@555 52
adamc@555 53 \begin{verbatim}
adamc@555 54 ./configure
adamc@555 55 make
adamc@555 56 sudo make install
adamc@555 57 \end{verbatim}
adamc@555 58
adam@1368 59 Some other packages must be installed for the above to work. At a minimum, you need a standard UNIX shell, with standard UNIX tools like sed and GCC in your execution path; MLton, the whole-program optimizing compiler for Standard ML; and the development files for the OpenSSL C library. As of this writing, in the ``testing'' version of Debian Linux, this command will install the more uncommon of these dependencies:
adamc@896 60 \begin{verbatim}
adam@1368 61 apt-get install mlton libssl-dev
adamc@896 62 \end{verbatim}
adamc@555 63
adamc@896 64 To build programs that access SQL databases, you also need one of these client libraries for supported backends.
adamc@555 65 \begin{verbatim}
adamc@896 66 apt-get install libpq-dev libmysqlclient15-dev libsqlite3-dev
adamc@555 67 \end{verbatim}
adamc@555 68
adamc@555 69 It is also possible to access the modules of the Ur/Web compiler interactively, within Standard ML of New Jersey. To install the prerequisites in Debian testing:
adamc@555 70 \begin{verbatim}
adamc@555 71 apt-get install smlnj libsmlnj-smlnj ml-yacc ml-lpt
adamc@555 72 \end{verbatim}
adamc@555 73
adamc@555 74 To begin an interactive session with the Ur compiler modules, run \texttt{make smlnj}, and then, from within an \texttt{sml} session, run \texttt{CM.make "src/urweb.cm";}. The \texttt{Compiler} module is the main entry point.
adamc@555 75
adamc@896 76 To run an SQL-backed application with a backend besides SQLite, you will probably want to install one of these servers.
adamc@555 77
adamc@555 78 \begin{verbatim}
adam@1400 79 apt-get install postgresql-8.4 mysql-server-5.1
adamc@555 80 \end{verbatim}
adamc@555 81
adamc@555 82 To use the Emacs mode, you must have a modern Emacs installed. We assume that you already know how to do this, if you're in the business of looking for an Emacs mode. The demo generation facility of the compiler will also call out to Emacs to syntax-highlight code, and that process depends on the \texttt{htmlize} module, which can be installed in Debian testing via:
adamc@555 83
adamc@555 84 \begin{verbatim}
adamc@555 85 apt-get install emacs-goodies-el
adamc@555 86 \end{verbatim}
adamc@555 87
adam@1441 88 If you don't want to install the Emacs mode, run \texttt{./configure} with the argument \texttt{--without-emacs}.
adam@1441 89
adamc@555 90 Even with the right packages installed, configuration and building might fail to work. After you run \texttt{./configure}, you will see the values of some named environment variables printed. You may need to adjust these values to get proper installation for your system. To change a value, store your preferred alternative in the corresponding UNIX environment variable, before running \texttt{./configure}. For instance, here is how to change the list of extra arguments that the Ur/Web compiler will pass to GCC on every invocation.
adamc@555 91
adamc@555 92 \begin{verbatim}
adamc@555 93 GCCARGS=-fnested-functions ./configure
adamc@555 94 \end{verbatim}
adamc@555 95
adam@1515 96 Some Mac OS X users have reported needing to use this particular GCCARGS value. Also, some older GCC versions have inlining-related bugs that can be masked (at some cost to output code quality) by adding \texttt{-fno-inline} here.
adamc@1137 97
adam@1464 98 Since the author is still getting a handle on the GNU Autotools that provide the build system, you may need to do some further work to get started, especially in environments with significant differences from Linux (where most testing is done). The variables \texttt{PGHEADER}, \texttt{MSHEADER}, and \texttt{SQHEADER} may be used to set the proper C header files to include for the development libraries of PostgreSQL, MySQL, and SQLite, respectively. To get libpq to link, one OS X user reported setting \texttt{GCCARGS="-I/opt/local/include -L/opt/local/lib/postgresql84"}, after creating a symbolic link with \texttt{ln -s /opt/local/include/postgresql84 /opt/local/include/postgresql}.
adamc@555 99
adamc@555 100 The Emacs mode can be set to autoload by adding the following to your \texttt{.emacs} file.
adamc@555 101
adamc@555 102 \begin{verbatim}
adamc@555 103 (add-to-list 'load-path "/usr/local/share/emacs/site-lisp/urweb-mode")
adamc@555 104 (load "urweb-mode-startup")
adamc@555 105 \end{verbatim}
adamc@555 106
adamc@555 107 Change the path in the first line if you chose a different Emacs installation path during configuration.
adamc@555 108
adamc@555 109
adamc@556 110 \section{Command-Line Compiler}
adamc@556 111
adamc@556 112 \subsection{Project Files}
adamc@556 113
adamc@556 114 The basic inputs to the \texttt{urweb} compiler are project files, which have the extension \texttt{.urp}. Here is a sample \texttt{.urp} file.
adamc@556 115
adamc@556 116 \begin{verbatim}
adamc@556 117 database dbname=test
adamc@556 118 sql crud1.sql
adamc@556 119
adamc@556 120 crud
adamc@556 121 crud1
adamc@556 122 \end{verbatim}
adamc@556 123
adamc@556 124 The \texttt{database} line gives the database information string to pass to libpq. In this case, the string only says to connect to a local database named \texttt{test}.
adamc@556 125
adamc@556 126 The \texttt{sql} line asks for an SQL source file to be generated, giving the commands to run to create the tables and sequences that this application expects to find. After building this \texttt{.urp} file, the following commands could be used to initialize the database, assuming that the current UNIX user exists as a Postgres user with database creation privileges:
adamc@556 127
adamc@556 128 \begin{verbatim}
adamc@556 129 createdb test
adamc@556 130 psql -f crud1.sql test
adamc@556 131 \end{verbatim}
adamc@556 132
adam@1331 133 A blank line separates the named directives from a list of modules to include in the project. Any line may contain a shell-script-style comment, where any suffix of a line starting at a hash character \texttt{\#} is ignored.
adamc@556 134
adamc@556 135 For each entry \texttt{M} in the module list, the file \texttt{M.urs} is included in the project if it exists, and the file \texttt{M.ur} must exist and is always included.
adamc@556 136
adamc@783 137 Here is the complete list of directive forms. ``FFI'' stands for ``foreign function interface,'' Ur's facility for interaction between Ur programs and C and JavaScript libraries.
adamc@783 138 \begin{itemize}
adam@1465 139 \item \texttt{[allow|deny] [url|mime|requestHeader|responseHeader] PATTERN} registers a rule governing which URLs, MIME types, HTTP request headers, or HTTP response headers are allowed to appear explicitly in this application. The first such rule to match a name determines the verdict. If \texttt{PATTERN} ends in \texttt{*}, it is interpreted as a prefix rule. Otherwise, a string must match it exactly.
adam@1400 140 \item \texttt{alwaysInline PATH} requests that every call to the referenced function be inlined. Section \ref{structure} explains how functions are assigned path strings.
adam@1462 141 \item \texttt{benignEffectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. Every effectful FFI function must be registered, or the optimizer may make invalid transformations. This version of the \texttt{effectful} directive registers that this function only has side effects that remain local to a single page generation.
adamc@783 142 \item \texttt{clientOnly Module.ident} registers an FFI function or transaction that may only be run in client browsers.
adamc@783 143 \item \texttt{clientToServer Module.ident} adds FFI type \texttt{Module.ident} to the list of types that are OK to marshal from clients to servers. Values like XML trees and SQL queries are hard to marshal without introducing expensive validity checks, so it's easier to ensure that the server never trusts clients to send such values. The file \texttt{include/urweb.h} shows examples of the C support functions that are required of any type that may be marshalled. These include \texttt{attrify}, \texttt{urlify}, and \texttt{unurlify} functions.
adamc@783 144 \item \texttt{database DBSTRING} sets the string to pass to libpq to open a database connection.
adamc@783 145 \item \texttt{debug} saves some intermediate C files, which is mostly useful to help in debugging the compiler itself.
adamc@783 146 \item \texttt{effectful Module.ident} registers an FFI function or transaction as having side effects. The optimizer avoids removing, moving, or duplicating calls to such functions. Every effectful FFI function must be registered, or the optimizer may make invalid transformations.
adamc@783 147 \item \texttt{exe FILENAME} sets the filename to which to write the output executable. The default for file \texttt{P.urp} is \texttt{P.exe}.
adamc@783 148 \item \texttt{ffi FILENAME} reads the file \texttt{FILENAME.urs} to determine the interface to a new FFI module. The name of the module is calculated from \texttt{FILENAME} in the same way as for normal source files. See the files \texttt{include/urweb.h} and \texttt{src/c/urweb.c} for examples of C headers and implementations for FFI modules. In general, every type or value \texttt{Module.ident} becomes \texttt{uw\_Module\_ident} in C.
adamc@1099 149 \item \texttt{include FILENAME} adds \texttt{FILENAME} to the list of files to be \texttt{\#include}d in C sources. This is most useful for interfacing with new FFI modules.
adamc@783 150 \item \texttt{jsFunc Module.ident=name} gives the JavaScript name of an FFI value.
adamc@1089 151 \item \texttt{library FILENAME} parses \texttt{FILENAME.urp} and merges its contents with the rest of the current file's contents. If \texttt{FILENAME.urp} doesn't exist, the compiler also tries \texttt{FILENAME/lib.urp}.
adam@1309 152 \item \texttt{limit class num} sets a resource usage limit for generated applications. The limit \texttt{class} will be set to the non-negative integer \texttt{num}. The classes are:
adam@1309 153 \begin{itemize}
adam@1309 154 \item \texttt{cleanup}: maximum number of cleanup operations (e.g., entries recording the need to deallocate certain temporary objects) that may be active at once per request
adam@1309 155 \item \texttt{database}: maximum size of database files (currently only used by SQLite)
adam@1309 156 \item \texttt{deltas}: maximum number of messages sendable in a single request handler with \texttt{Basis.send}
adam@1309 157 \item \texttt{globals}: maximum number of global variables that FFI libraries may set in a single request context
adam@1309 158 \item \texttt{headers}: maximum size (in bytes) of per-request buffer used to hold HTTP headers for generated pages
adam@1309 159 \item \texttt{heap}: maximum size (in bytes) of per-request heap for dynamically-allocated data
adam@1309 160 \item \texttt{inputs}: maximum number of top-level form fields per request
adam@1309 161 \item \texttt{messages}: maximum size (in bytes) of per-request buffer used to hold a single outgoing message sent with \texttt{Basis.send}
adam@1309 162 \item \texttt{page}: maximum size (in bytes) of per-request buffer used to hold HTML content of generated pages
adam@1309 163 \item \texttt{script}: maximum size (in bytes) of per-request buffer used to hold JavaScript content of generated pages
adam@1309 164 \item \texttt{subinputs}: maximum number of form fields per request, excluding top-level fields
adam@1309 165 \item \texttt{time}: maximum running time of a single page request, in units of approximately 0.1 seconds
adam@1309 166 \item \texttt{transactionals}: maximum number of custom transactional actions (e.g., sending an e-mail) that may be run in a single page generation
adam@1309 167 \end{itemize}
adamc@783 168 \item \texttt{link FILENAME} adds \texttt{FILENAME} to the list of files to be passed to the GCC linker at the end of compilation. This is most useful for importing extra libraries needed by new FFI modules.
adam@1332 169 \item \texttt{minHeap NUMBYTES} sets the initial size for thread-local heaps used in handling requests. These heaps grow automatically as needed (up to any maximum set with \texttt{limit}), but each regrow requires restarting the request handling process.
adam@1478 170 \item \texttt{noXsrfProtection URIPREFIX} turns off automatic cross-site request forgery protection for the page handler identified by the given URI prefix. This will avoid checking cryptographic signatures on cookies, which is generally a reasonable idea for some pages, such as login pages that are going to discard all old cookie values, anyway.
adam@1297 171 \item \texttt{onError Module.var} changes the handling of fatal application errors. Instead of displaying a default, ugly error 500 page, the error page will be generated by calling function \texttt{Module.var} on a piece of XML representing the error message. The error handler should have type $\mt{xbody} \to \mt{transaction} \; \mt{page}$. Note that the error handler \emph{cannot} be in the application's main module, since that would register it as explicitly callable via URLs.
adamc@852 172 \item \texttt{path NAME=VALUE} creates a mapping from \texttt{NAME} to \texttt{VALUE}. This mapping may be used at the beginnings of filesystem paths given to various other configuration directives. A path like \texttt{\$NAME/rest} is expanded to \texttt{VALUE/rest}. There is an initial mapping from the empty name (for paths like \texttt{\$/list}) to the directory where the Ur/Web standard library is installed. If you accept the default \texttt{configure} options, this directory is \texttt{/usr/local/lib/urweb/ur}.
adamc@783 173 \item \texttt{prefix PREFIX} sets the prefix included before every URI within the generated application. The default is \texttt{/}.
adamc@783 174 \item \texttt{profile} generates an executable that may be used with gprof.
adam@1300 175 \item \texttt{rewrite KIND FROM TO} gives a rule for rewriting canonical module paths. For instance, the canonical path of a page may be \texttt{Mod1.Mod2.mypage}, while you would rather the page were accessed via a URL containing only \texttt{page}. The directive \texttt{rewrite url Mod1/Mod2/mypage page} would accomplish that. The possible values of \texttt{KIND} determine which kinds of objects are affected. The kind \texttt{all} matches any object, and \texttt{url} matches page URLs. The kinds \texttt{table}, \texttt{sequence}, and \texttt{view} match those sorts of SQL entities, and \texttt{relation} matches any of those three. \texttt{cookie} matches HTTP cookies, and \texttt{style} matches CSS class names. If \texttt{FROM} ends in \texttt{/*}, it is interpreted as a prefix matching rule, and rewriting occurs by replacing only the appropriate prefix of a path with \texttt{TO}. The \texttt{TO} field may be left empty to express the idea of deleting a prefix. For instance, \texttt{rewrite url Main/*} will strip all \texttt{Main/} prefixes from URLs. While the actual external names of relations and styles have parts separated by underscores instead of slashes, all rewrite rules must be written in terms of slashes.
adamc@1183 176 \item \texttt{safeGet URI} asks to allow the page handler assigned this canonical URI prefix to cause persistent side effects, even if accessed via an HTTP \cd{GET} request.
adamc@783 177 \item \texttt{script URL} adds \texttt{URL} to the list of extra JavaScript files to be included at the beginning of any page that uses JavaScript. This is most useful for importing JavaScript versions of functions found in new FFI modules.
adamc@783 178 \item \texttt{serverOnly Module.ident} registers an FFI function or transaction that may only be run on the server.
adamc@1164 179 \item \texttt{sigfile PATH} sets a path where your application should look for a key to use in cryptographic signing. This is used to prevent cross-site request forgery attacks for any form handler that both reads a cookie and creates side effects. If the referenced file doesn't exist, an application will create it and read its saved data on future invocations. You can also initialize the file manually with any contents at least 16 bytes long; the first 16 bytes will be treated as the key.
adamc@783 180 \item \texttt{sql FILENAME} sets where to write an SQL file with the commands to create the expected database schema. The default is not to create such a file.
adamc@783 181 \item \texttt{timeout N} sets to \texttt{N} seconds the amount of time that the generated server will wait after the last contact from a client before determining that that client has exited the application. Clients that remain active will take the timeout setting into account in determining how often to ping the server, so it only makes sense to set a high timeout to cope with browser and network delays and failures. Higher timeouts can lead to more unnecessary client information taking up memory on the server. The timeout goes unused by any page that doesn't involve the \texttt{recv} function, since the server only needs to store per-client information for clients that receive asynchronous messages.
adamc@783 182 \end{itemize}
adamc@701 183
adamc@701 184
adamc@557 185 \subsection{Building an Application}
adamc@557 186
adamc@557 187 To compile project \texttt{P.urp}, simply run
adamc@557 188 \begin{verbatim}
adamc@557 189 urweb P
adamc@557 190 \end{verbatim}
adamc@1198 191 The output executable is a standalone web server. Run it with the command-line argument \texttt{-h} to see which options it takes. If the project file lists a database, the web server will attempt to connect to that database on startup. See Section \ref{structure} for an explanation of the URI mapping convention, which determines how each page of your application may be accessed via URLs.
adamc@557 192
adamc@557 193 To time how long the different compiler phases run, without generating an executable, run
adamc@557 194 \begin{verbatim}
adamc@557 195 urweb -timing P
adamc@557 196 \end{verbatim}
adamc@557 197
adamc@1086 198 To stop the compilation process after type-checking, run
adamc@1086 199 \begin{verbatim}
adamc@1086 200 urweb -tc P
adamc@1086 201 \end{verbatim}
adamc@1086 202
adamc@1170 203 To output information relevant to CSS stylesheets (and not finish regular compilation), run
adamc@1170 204 \begin{verbatim}
adamc@1170 205 urweb -css P
adamc@1170 206 \end{verbatim}
adamc@1170 207 The first output line is a list of categories of CSS properties that would be worth setting on the document body. The remaining lines are space-separated pairs of CSS class names and categories of properties that would be worth setting for that class. The category codes are divided into two varieties. Codes that reveal properties of a tag or its (recursive) children are \cd{B} for block-level elements, \cd{C} for table captions, \cd{D} for table cells, \cd{L} for lists, and \cd{T} for tables. Codes that reveal properties of the precise tag that uses a class are \cd{b} for block-level elements, \cd{t} for tables, \cd{d} for table cells, \cd{-} for table rows, \cd{H} for the possibility to set a height, \cd{N} for non-replaced inline-level elements, \cd{R} for replaced inline elements, and \cd{W} for the possibility to set a width.
adamc@1170 208
adamc@896 209 Some other command-line parameters are accepted:
adamc@896 210 \begin{itemize}
adamc@896 211 \item \texttt{-db <DBSTRING>}: Set database connection information, using the format expected by Postgres's \texttt{PQconnectdb()}, which is \texttt{name1=value1 ... nameN=valueN}. The same format is also parsed and used to discover connection parameters for MySQL and SQLite. The only significant settings for MySQL are \texttt{host}, \texttt{hostaddr}, \texttt{port}, \texttt{dbname}, \texttt{user}, and \texttt{password}. The only significant setting for SQLite is \texttt{dbname}, which is interpreted as the filesystem path to the database. Additionally, when using SQLite, a database string may be just a file path.
adamc@896 212
adamc@896 213 \item \texttt{-dbms [postgres|mysql|sqlite]}: Sets the database backend to use.
adamc@896 214 \begin{itemize}
adamc@896 215 \item \texttt{postgres}: This is PostgreSQL, the default. Among the supported engines, Postgres best matches the design philosophy behind Ur, with a focus on consistent views of data, even in the face of much concurrency. Different database engines have different quirks of SQL syntax. Ur/Web tends to use Postgres idioms where there are choices to be made, though the compiler translates SQL as needed to support other backends.
adamc@896 216
adamc@896 217 A command sequence like this can initialize a Postgres database, using a file \texttt{app.sql} generated by the compiler:
adamc@896 218 \begin{verbatim}
adamc@896 219 createdb app
adamc@896 220 psql -f app.sql app
adamc@896 221 \end{verbatim}
adamc@896 222
adamc@896 223 \item \texttt{mysql}: This is MySQL, another popular relational database engine that uses persistent server processes. Ur/Web needs transactions to function properly. Many installations of MySQL use non-transactional storage engines by default. Ur/Web generates table definitions that try to use MySQL's InnoDB engine, which supports transactions. You can edit the first line of a generated \texttt{.sql} file to change this behavior, but it really is true that Ur/Web applications will exhibit bizarre behavior if you choose an engine that ignores transaction commands.
adamc@896 224
adamc@896 225 A command sequence like this can initialize a MySQL database:
adamc@896 226 \begin{verbatim}
adamc@896 227 echo "CREATE DATABASE app" | mysql
adamc@896 228 mysql -D app <app.sql
adamc@896 229 \end{verbatim}
adamc@896 230
adamc@896 231 \item \texttt{sqlite}: This is SQLite, a simple filesystem-based transactional database engine. With this backend, Ur/Web applications can run without any additional server processes. The other engines are generally preferred for large-workload performance and full admin feature sets, while SQLite is popular for its low resource footprint and ease of set-up.
adamc@896 232
adamc@896 233 A command like this can initialize an SQLite database:
adamc@896 234 \begin{verbatim}
adamc@896 235 sqlite3 path/to/database/file <app.sql
adamc@896 236 \end{verbatim}
adamc@896 237 \end{itemize}
adamc@896 238
adam@1309 239 \item \texttt{-limit class num}: Equivalent to the \texttt{limit} directive from \texttt{.urp} files
adam@1309 240
adamc@896 241 \item \texttt{-output FILENAME}: Set where the application executable is written.
adamc@896 242
adamc@1127 243 \item \texttt{-path NAME VALUE}: Set the value of path variable \texttt{\$NAME} to \texttt{VALUE}, for use in \texttt{.urp} files.
adamc@1127 244
adam@1335 245 \item \texttt{-prefix PREFIX}: Equivalent to the \texttt{prefix} directive from \texttt{.urp} files
adam@1335 246
adamc@896 247 \item \texttt{-protocol [http|cgi|fastcgi]}: Set the protocol that the generated application speaks.
adamc@896 248 \begin{itemize}
adamc@896 249 \item \texttt{http}: This is the default. It is for building standalone web servers that can be accessed by web browsers directly.
adamc@896 250
adamc@896 251 \item \texttt{cgi}: This is the classic protocol that web servers use to generate dynamic content by spawning new processes. While Ur/Web programs may in general use message-passing with the \texttt{send} and \texttt{recv} functions, that functionality is not yet supported in CGI, since CGI needs a fresh process for each request, and message-passing needs to use persistent sockets to deliver messages.
adamc@896 252
adamc@896 253 Since Ur/Web treats paths in an unusual way, a configuration line like this one can be used to configure an application that was built with URL prefix \texttt{/Hello}:
adamc@896 254 \begin{verbatim}
adamc@896 255 ScriptAlias /Hello /path/to/hello.exe
adamc@896 256 \end{verbatim}
adamc@896 257
adamc@1163 258 A different method can be used for, e.g., a shared host, where you can only configure Apache via \texttt{.htaccess} files. Drop the generated executable into your web space and mark it as CGI somehow. For instance, if the script ends in \texttt{.exe}, you might put this in \texttt{.htaccess} in the directory containing the script:
adamc@1163 259 \begin{verbatim}
adamc@1163 260 Options +ExecCGI
adamc@1163 261 AddHandler cgi-script .exe
adamc@1163 262 \end{verbatim}
adamc@1163 263
adamc@1163 264 Additionally, make sure that Ur/Web knows the proper URI prefix for your script. For instance, if the script is accessed via \texttt{http://somewhere/dir/script.exe}, then include this line in your \texttt{.urp} file:
adamc@1163 265 \begin{verbatim}
adamc@1163 266 prefix /dir/script.exe/
adamc@1163 267 \end{verbatim}
adamc@1163 268
adamc@1163 269 To access the \texttt{foo} function in the \texttt{Bar} module, you would then hit \texttt{http://somewhere/dir/script.exe/Bar/foo}.
adamc@1163 270
adamc@1164 271 If your application contains form handlers that read cookies before causing side effects, then you will need to use the \texttt{sigfile} \texttt{.urp} directive, too.
adamc@1164 272
adamc@896 273 \item \texttt{fastcgi}: This is a newer protocol inspired by CGI, wherein web servers can start and reuse persistent external processes to generate dynamic content. Ur/Web doesn't implement the whole protocol, but Ur/Web's support has been tested to work with the \texttt{mod\_fastcgi}s of Apache and lighttpd.
adamc@896 274
adamc@896 275 To configure a FastCGI program with Apache, one could combine the above \texttt{ScriptAlias} line with a line like this:
adamc@896 276 \begin{verbatim}
adamc@896 277 FastCgiServer /path/to/hello.exe -idle-timeout 99999
adamc@896 278 \end{verbatim}
adamc@896 279 The idle timeout is only important for applications that use message-passing. Client connections may go long periods without receiving messages, and Apache tries to be helpful and garbage collect them in such cases. To prevent that behavior, we specify how long a connection must be idle to be collected.
adamc@896 280
adamc@896 281 Here is some lighttpd configuration for the same application.
adamc@896 282 \begin{verbatim}
adamc@896 283 fastcgi.server = (
adamc@896 284 "/Hello/" =>
adamc@896 285 (( "bin-path" => "/path/to/hello.exe",
adamc@896 286 "socket" => "/tmp/hello",
adamc@896 287 "check-local" => "disable",
adamc@896 288 "docroot" => "/",
adamc@896 289 "max-procs" => "1"
adamc@896 290 ))
adamc@896 291 )
adamc@896 292 \end{verbatim}
adamc@896 293 The least obvious requirement is setting \texttt{max-procs} to 1, so that lighttpd doesn't try to multiplex requests across multiple external processes. This is required for message-passing applications, where a single database of client connections is maintained within a multi-threaded server process. Multiple processes may, however, be used safely with applications that don't use message-passing.
adamc@896 294
adamc@896 295 A FastCGI process reads the environment variable \texttt{URWEB\_NUM\_THREADS} to determine how many threads to spawn for handling client requests. The default is 1.
adam@1509 296
adam@1509 297 \item \texttt{static}: This protocol may be used to generate static web pages from Ur/Web code. The output executable expects a single command-line argument, giving the URI of a page to generate. For instance, this argument might be \cd{/main}, in which case a static HTTP response for that page will be written to stdout.
adamc@896 298 \end{itemize}
adamc@896 299
adamc@1127 300 \item \texttt{-root Name PATH}: Trigger an alternate module convention for all source files found in directory \texttt{PATH} or any of its subdirectories. Any file \texttt{PATH/foo.ur} defines a module \texttt{Name.Foo} instead of the usual \texttt{Foo}. Any file \texttt{PATH/subdir/foo.ur} defines a module \texttt{Name.Subdir.Foo}, and so on for arbitrary nesting of subdirectories.
adamc@1127 301
adamc@1164 302 \item \texttt{-sigfile PATH}: Same as the \texttt{sigfile} directive in \texttt{.urp} files
adamc@1164 303
adamc@896 304 \item \texttt{-sql FILENAME}: Set where a database set-up SQL script is written.
adamc@1095 305
adamc@1095 306 \item \texttt{-static}: Link the runtime system statically. The default is to link against dynamic libraries.
adamc@896 307 \end{itemize}
adamc@896 308
adam@1297 309 There is an additional convenience method for invoking \texttt{urweb}. If the main argument is \texttt{FOO}, and \texttt{FOO.ur} exists but \texttt{FOO.urp} doesn't, then the invocation is interpreted as if called on a \texttt{.urp} file containing \texttt{FOO} as its only main entry, with an additional \texttt{rewrite all FOO/*} directive.
adamc@556 310
adam@1509 311 \subsection{Tutorial Formatting}
adam@1509 312
adam@1509 313 The Ur/Web compiler also supports rendering of nice HTML tutorials from Ur source files, when invoked like \cd{urweb -tutorial DIR}. The directory \cd{DIR} is examined for files whose names end in \cd{.ur}. Every such file is translated into a \cd{.html} version.
adam@1509 314
adam@1509 315 These input files follow normal Ur syntax, with a few exceptions:
adam@1509 316 \begin{itemize}
adam@1509 317 \item The first line must be a comment like \cd{(* TITLE *)}, where \cd{TITLE} is a string of your choice that will be used as the title of the output page.
adam@1509 318 \item While most code in the output HTML will be formatted as a monospaced code listing, text in regular Ur comments is formatted as normal English text.
adam@1509 319 \item A comment like \cd{(* * HEADING *)} introduces a section heading, with text \cd{HEADING} of your choice.
adam@1509 320 \item To include both a rendering of an Ur expression and a pretty-printed version of its value, bracket the expression with \cd{(* begin eval *)} and \cd{(* end *)}. The result of expression evaluation is pretty-printed with \cd{show}, so the expression type must belong to that type class.
adam@1509 321 \item To include code that should not be shown in the tutorial (e.g., to add a \cd{show} instance to use with \cd{eval}), bracket the code with \cd{(* begin hide *)} and \cd{(* end *)}.
adam@1509 322 \end{itemize}
adam@1509 323
adam@1509 324 A word of warning: as for demo generation, tutorial generation calls Emacs to syntax-highlight Ur code.
adam@1509 325
adam@1509 326
adamc@529 327 \section{Ur Syntax}
adamc@529 328
adamc@784 329 In this section, we describe the syntax of Ur, deferring to a later section discussion of most of the syntax specific to SQL and XML. The sole exceptions are the declaration forms for relations, cookies, and styles.
adamc@524 330
adamc@524 331 \subsection{Lexical Conventions}
adamc@524 332
adamc@524 333 We give the Ur language definition in \LaTeX $\;$ math mode, since that is prettier than monospaced ASCII. The corresponding ASCII syntax can be read off directly. Here is the key for mapping math symbols to ASCII character sequences.
adamc@524 334
adamc@524 335 \begin{center}
adamc@524 336 \begin{tabular}{rl}
adamc@524 337 \textbf{\LaTeX} & \textbf{ASCII} \\
adamc@524 338 $\to$ & \cd{->} \\
adamc@652 339 $\longrightarrow$ & \cd{-->} \\
adamc@524 340 $\times$ & \cd{*} \\
adamc@524 341 $\lambda$ & \cd{fn} \\
adamc@524 342 $\Rightarrow$ & \cd{=>} \\
adamc@652 343 $\Longrightarrow$ & \cd{==>} \\
adamc@529 344 $\neq$ & \cd{<>} \\
adamc@529 345 $\leq$ & \cd{<=} \\
adamc@529 346 $\geq$ & \cd{>=} \\
adamc@524 347 \\
adamc@524 348 $x$ & Normal textual identifier, not beginning with an uppercase letter \\
adamc@525 349 $X$ & Normal textual identifier, beginning with an uppercase letter \\
adamc@524 350 \end{tabular}
adamc@524 351 \end{center}
adamc@524 352
adamc@525 353 We often write syntax like $e^*$ to indicate zero or more copies of $e$, $e^+$ to indicate one or more copies, and $e,^*$ and $e,^+$ to indicate multiple copies separated by commas. Another separator may be used in place of a comma. The $e$ term may be surrounded by parentheses to indicate grouping; those parentheses should not be included in the actual ASCII.
adamc@524 354
adamc@873 355 We write $\ell$ for literals of the primitive types, for the most part following C conventions. There are $\mt{int}$, $\mt{float}$, $\mt{char}$, and $\mt{string}$ literals. Character literals follow the SML convention instead of the C convention, written like \texttt{\#"a"} instead of \texttt{'a'}.
adamc@526 356
adamc@527 357 This version of the manual doesn't include operator precedences; see \texttt{src/urweb.grm} for that.
adamc@527 358
adam@1297 359 As in the ML language family, the syntax \texttt{(* ... *)} is used for (nestable) comments. Within XML literals, Ur/Web also supports the usual \texttt{<!-- ... -->} XML comments.
adam@1297 360
adamc@552 361 \subsection{\label{core}Core Syntax}
adamc@524 362
adamc@524 363 \emph{Kinds} classify types and other compile-time-only entities. Each kind in the grammar is listed with a description of the sort of data it classifies.
adamc@524 364 $$\begin{array}{rrcll}
adamc@524 365 \textrm{Kinds} & \kappa &::=& \mt{Type} & \textrm{proper types} \\
adamc@525 366 &&& \mt{Unit} & \textrm{the trivial constructor} \\
adamc@525 367 &&& \mt{Name} & \textrm{field names} \\
adamc@525 368 &&& \kappa \to \kappa & \textrm{type-level functions} \\
adamc@525 369 &&& \{\kappa\} & \textrm{type-level records} \\
adamc@525 370 &&& (\kappa\times^+) & \textrm{type-level tuples} \\
adamc@652 371 &&& X & \textrm{variable} \\
adamc@652 372 &&& X \longrightarrow k & \textrm{kind-polymorphic type-level function} \\
adamc@529 373 &&& \_\_ & \textrm{wildcard} \\
adamc@525 374 &&& (\kappa) & \textrm{explicit precedence} \\
adamc@524 375 \end{array}$$
adamc@524 376
adamc@524 377 Ur supports several different notions of functions that take types as arguments. These arguments can be either implicit, causing them to be inferred at use sites; or explicit, forcing them to be specified manually at use sites. There is a common explicitness annotation convention applied at the definitions of and in the types of such functions.
adamc@524 378 $$\begin{array}{rrcll}
adamc@524 379 \textrm{Explicitness} & ? &::=& :: & \textrm{explicit} \\
adamc@558 380 &&& ::: & \textrm{implicit}
adamc@524 381 \end{array}$$
adamc@524 382
adamc@524 383 \emph{Constructors} are the main class of compile-time-only data. They include proper types and are classified by kinds.
adamc@524 384 $$\begin{array}{rrcll}
adamc@524 385 \textrm{Constructors} & c, \tau &::=& (c) :: \kappa & \textrm{kind annotation} \\
adamc@530 386 &&& \hat{x} & \textrm{constructor variable} \\
adamc@524 387 \\
adamc@525 388 &&& \tau \to \tau & \textrm{function type} \\
adamc@525 389 &&& x \; ? \; \kappa \to \tau & \textrm{polymorphic function type} \\
adamc@652 390 &&& X \longrightarrow \tau & \textrm{kind-polymorphic function type} \\
adamc@525 391 &&& \$ c & \textrm{record type} \\
adamc@524 392 \\
adamc@525 393 &&& c \; c & \textrm{type-level function application} \\
adamc@530 394 &&& \lambda x \; :: \; \kappa \Rightarrow c & \textrm{type-level function abstraction} \\
adamc@524 395 \\
adamc@652 396 &&& X \Longrightarrow c & \textrm{type-level kind-polymorphic function abstraction} \\
adamc@655 397 &&& c [\kappa] & \textrm{type-level kind-polymorphic function application} \\
adamc@652 398 \\
adamc@525 399 &&& () & \textrm{type-level unit} \\
adamc@525 400 &&& \#X & \textrm{field name} \\
adamc@524 401 \\
adamc@525 402 &&& [(c = c)^*] & \textrm{known-length type-level record} \\
adamc@525 403 &&& c \rc c & \textrm{type-level record concatenation} \\
adamc@652 404 &&& \mt{map} & \textrm{type-level record map} \\
adamc@524 405 \\
adamc@558 406 &&& (c,^+) & \textrm{type-level tuple} \\
adamc@525 407 &&& c.n & \textrm{type-level tuple projection ($n \in \mathbb N^+$)} \\
adamc@524 408 \\
adamc@652 409 &&& [c \sim c] \Rightarrow \tau & \textrm{guarded type} \\
adamc@524 410 \\
adamc@529 411 &&& \_ :: \kappa & \textrm{wildcard} \\
adamc@525 412 &&& (c) & \textrm{explicit precedence} \\
adamc@530 413 \\
adamc@530 414 \textrm{Qualified uncapitalized variables} & \hat{x} &::=& x & \textrm{not from a module} \\
adamc@530 415 &&& M.x & \textrm{projection from a module} \\
adamc@525 416 \end{array}$$
adamc@525 417
adamc@655 418 We include both abstraction and application for kind polymorphism, but applications are only inferred internally; they may not be written explicitly in source programs.
adamc@655 419
adamc@525 420 Modules of the module system are described by \emph{signatures}.
adamc@525 421 $$\begin{array}{rrcll}
adamc@525 422 \textrm{Signatures} & S &::=& \mt{sig} \; s^* \; \mt{end} & \textrm{constant} \\
adamc@525 423 &&& X & \textrm{variable} \\
adamc@525 424 &&& \mt{functor}(X : S) : S & \textrm{functor} \\
adamc@529 425 &&& S \; \mt{where} \; \mt{con} \; x = c & \textrm{concretizing an abstract constructor} \\
adamc@525 426 &&& M.X & \textrm{projection from a module} \\
adamc@525 427 \\
adamc@525 428 \textrm{Signature items} & s &::=& \mt{con} \; x :: \kappa & \textrm{abstract constructor} \\
adamc@525 429 &&& \mt{con} \; x :: \kappa = c & \textrm{concrete constructor} \\
adamc@528 430 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 431 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@525 432 &&& \mt{val} \; x : \tau & \textrm{value} \\
adamc@525 433 &&& \mt{structure} \; X : S & \textrm{sub-module} \\
adamc@525 434 &&& \mt{signature} \; X = S & \textrm{sub-signature} \\
adamc@525 435 &&& \mt{include} \; S & \textrm{signature inclusion} \\
adamc@525 436 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@654 437 &&& \mt{class} \; x :: \kappa & \textrm{abstract constructor class} \\
adamc@654 438 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@525 439 \\
adamc@525 440 \textrm{Datatype constructors} & dc &::=& X & \textrm{nullary constructor} \\
adamc@525 441 &&& X \; \mt{of} \; \tau & \textrm{unary constructor} \\
adamc@524 442 \end{array}$$
adamc@524 443
adamc@526 444 \emph{Patterns} are used to describe structural conditions on expressions, such that expressions may be tested against patterns, generating assignments to pattern variables if successful.
adamc@526 445 $$\begin{array}{rrcll}
adamc@526 446 \textrm{Patterns} & p &::=& \_ & \textrm{wildcard} \\
adamc@526 447 &&& x & \textrm{variable} \\
adamc@526 448 &&& \ell & \textrm{constant} \\
adamc@526 449 &&& \hat{X} & \textrm{nullary constructor} \\
adamc@526 450 &&& \hat{X} \; p & \textrm{unary constructor} \\
adamc@526 451 &&& \{(x = p,)^*\} & \textrm{rigid record pattern} \\
adamc@526 452 &&& \{(x = p,)^+, \ldots\} & \textrm{flexible record pattern} \\
adamc@852 453 &&& p : \tau & \textrm{type annotation} \\
adamc@527 454 &&& (p) & \textrm{explicit precedence} \\
adamc@526 455 \\
adamc@529 456 \textrm{Qualified capitalized variables} & \hat{X} &::=& X & \textrm{not from a module} \\
adamc@526 457 &&& M.X & \textrm{projection from a module} \\
adamc@526 458 \end{array}$$
adamc@526 459
adamc@527 460 \emph{Expressions} are the main run-time entities, corresponding to both ``expressions'' and ``statements'' in mainstream imperative languages.
adamc@527 461 $$\begin{array}{rrcll}
adamc@527 462 \textrm{Expressions} & e &::=& e : \tau & \textrm{type annotation} \\
adamc@529 463 &&& \hat{x} & \textrm{variable} \\
adamc@529 464 &&& \hat{X} & \textrm{datatype constructor} \\
adamc@527 465 &&& \ell & \textrm{constant} \\
adamc@527 466 \\
adamc@527 467 &&& e \; e & \textrm{function application} \\
adamc@527 468 &&& \lambda x : \tau \Rightarrow e & \textrm{function abstraction} \\
adamc@527 469 &&& e [c] & \textrm{polymorphic function application} \\
adamc@852 470 &&& \lambda [x \; ? \; \kappa] \Rightarrow e & \textrm{polymorphic function abstraction} \\
adamc@655 471 &&& e [\kappa] & \textrm{kind-polymorphic function application} \\
adamc@652 472 &&& X \Longrightarrow e & \textrm{kind-polymorphic function abstraction} \\
adamc@527 473 \\
adamc@527 474 &&& \{(c = e,)^*\} & \textrm{known-length record} \\
adamc@527 475 &&& e.c & \textrm{record field projection} \\
adamc@527 476 &&& e \rc e & \textrm{record concatenation} \\
adamc@527 477 &&& e \rcut c & \textrm{removal of a single record field} \\
adamc@527 478 &&& e \rcutM c & \textrm{removal of multiple record fields} \\
adamc@527 479 \\
adamc@527 480 &&& \mt{let} \; ed^* \; \mt{in} \; e \; \mt{end} & \textrm{local definitions} \\
adamc@527 481 \\
adamc@527 482 &&& \mt{case} \; e \; \mt{of} \; (p \Rightarrow e|)^+ & \textrm{pattern matching} \\
adamc@527 483 \\
adamc@654 484 &&& \lambda [c \sim c] \Rightarrow e & \textrm{guarded expression abstraction} \\
adamc@654 485 &&& e \; ! & \textrm{guarded expression application} \\
adamc@527 486 \\
adamc@527 487 &&& \_ & \textrm{wildcard} \\
adamc@527 488 &&& (e) & \textrm{explicit precedence} \\
adamc@527 489 \\
adamc@527 490 \textrm{Local declarations} & ed &::=& \cd{val} \; x : \tau = e & \textrm{non-recursive value} \\
adamc@527 491 &&& \cd{val} \; \cd{rec} \; (x : \tau = e \; \cd{and})^+ & \textrm{mutually-recursive values} \\
adamc@527 492 \end{array}$$
adamc@527 493
adamc@655 494 As with constructors, we include both abstraction and application for kind polymorphism, but applications are only inferred internally.
adamc@655 495
adamc@528 496 \emph{Declarations} primarily bring new symbols into context.
adamc@528 497 $$\begin{array}{rrcll}
adamc@528 498 \textrm{Declarations} & d &::=& \mt{con} \; x :: \kappa = c & \textrm{constructor synonym} \\
adamc@528 499 &&& \mt{datatype} \; x \; x^* = dc\mid^+ & \textrm{algebraic datatype definition} \\
adamc@529 500 &&& \mt{datatype} \; x = \mt{datatype} \; M.x & \textrm{algebraic datatype import} \\
adamc@528 501 &&& \mt{val} \; x : \tau = e & \textrm{value} \\
adamc@528 502 &&& \mt{val} \; \cd{rec} \; (x : \tau = e \; \mt{and})^+ & \textrm{mutually-recursive values} \\
adamc@528 503 &&& \mt{structure} \; X : S = M & \textrm{module definition} \\
adamc@528 504 &&& \mt{signature} \; X = S & \textrm{signature definition} \\
adamc@528 505 &&& \mt{open} \; M & \textrm{module inclusion} \\
adamc@528 506 &&& \mt{constraint} \; c \sim c & \textrm{record disjointness constraint} \\
adamc@528 507 &&& \mt{open} \; \mt{constraints} \; M & \textrm{inclusion of just the constraints from a module} \\
adamc@528 508 &&& \mt{table} \; x : c & \textrm{SQL table} \\
adamc@784 509 &&& \mt{view} \; x : c & \textrm{SQL view} \\
adamc@528 510 &&& \mt{sequence} \; x & \textrm{SQL sequence} \\
adamc@535 511 &&& \mt{cookie} \; x : \tau & \textrm{HTTP cookie} \\
adamc@784 512 &&& \mt{style} \; x : \tau & \textrm{CSS class} \\
adamc@654 513 &&& \mt{class} \; x :: \kappa = c & \textrm{concrete constructor class} \\
adamc@1085 514 &&& \mt{task} \; e = e & \textrm{recurring task} \\
adamc@528 515 \\
adamc@529 516 \textrm{Modules} & M &::=& \mt{struct} \; d^* \; \mt{end} & \textrm{constant} \\
adamc@529 517 &&& X & \textrm{variable} \\
adamc@529 518 &&& M.X & \textrm{projection} \\
adamc@529 519 &&& M(M) & \textrm{functor application} \\
adamc@529 520 &&& \mt{functor}(X : S) : S = M & \textrm{functor abstraction} \\
adamc@528 521 \end{array}$$
adamc@528 522
adamc@528 523 There are two kinds of Ur files. A file named $M\texttt{.ur}$ is an \emph{implementation file}, and it should contain a sequence of declarations $d^*$. A file named $M\texttt{.urs}$ is an \emph{interface file}; it must always have a matching $M\texttt{.ur}$ and should contain a sequence of signature items $s^*$. When both files are present, the overall effect is the same as a monolithic declaration $\mt{structure} \; M : \mt{sig} \; s^* \; \mt{end} = \mt{struct} \; d^* \; \mt{end}$. When no interface file is included, the overall effect is similar, with a signature for module $M$ being inferred rather than just checked against an interface.
adamc@527 524
adamc@784 525 We omit some extra possibilities in $\mt{table}$ syntax, deferring them to Section \ref{tables}.
adamc@784 526
adamc@529 527 \subsection{Shorthands}
adamc@529 528
adamc@529 529 There are a variety of derived syntactic forms that elaborate into the core syntax from the last subsection. We will present the additional forms roughly following the order in which we presented the constructs that they elaborate into.
adamc@529 530
adamc@529 531 In many contexts where record fields are expected, like in a projection $e.c$, a constant field may be written as simply $X$, rather than $\#X$.
adamc@529 532
adamc@529 533 A record type may be written $\{(c = c,)^*\}$, which elaborates to $\$[(c = c,)^*]$.
adamc@529 534
adamc@533 535 The notation $[c_1, \ldots, c_n]$ is shorthand for $[c_1 = (), \ldots, c_n = ()]$.
adamc@533 536
adam@1350 537 A tuple type $\tau_1 \times \ldots \times \tau_n$ expands to a record type $\{1 : \tau_1, \ldots, n : \tau_n\}$, with natural numbers as field names. A tuple expression $(e_1, \ldots, e_n)$ expands to a record expression $\{1 = e_1, \ldots, n = e_n\}$. A tuple pattern $(p_1, \ldots, p_n)$ expands to a rigid record pattern $\{1 = p_1, \ldots, n = p_n\}$. Positive natural numbers may be used in most places where field names would be allowed.
adamc@529 538
adamc@852 539 In general, several adjacent $\lambda$ forms may be combined into one, and kind and type annotations may be omitted, in which case they are implicitly included as wildcards. More formally, for constructor-level abstractions, we can define a new non-terminal $b ::= x \mid (x :: \kappa) \mid X$ and allow composite abstractions of the form $\lambda b^+ \Rightarrow c$, elaborating into the obvious sequence of one core $\lambda$ per element of $b^+$.
adamc@529 540
adam@1306 541 In some contexts, the parser isn't happy with token sequences like $x :: \_$, to indicate a constructor variable of wildcard kind. In such cases, write the second two tokens as $::\hspace{-.05in}\_$, with no intervening spaces. Analogous syntax $:::\hspace{-.05in}\_$ is available for implicit constructor arguments.
adam@1302 542
adamc@529 543 For any signature item or declaration that defines some entity to be equal to $A$ with classification annotation $B$ (e.g., $\mt{val} \; x : B = A$), $B$ and the preceding colon (or similar punctuation) may be omitted, in which case it is filled in as a wildcard.
adamc@529 544
adamc@529 545 A signature item or declaration $\mt{type} \; x$ or $\mt{type} \; x = \tau$ is elaborated into $\mt{con} \; x :: \mt{Type}$ or $\mt{con} \; x :: \mt{Type} = \tau$, respectively.
adamc@529 546
adamc@654 547 A signature item or declaration $\mt{class} \; x = \lambda y \Rightarrow c$ may be abbreviated $\mt{class} \; x \; y = c$.
adamc@529 548
adam@1482 549 Handling of implicit and explicit constructor arguments may be tweaked with some prefixes to variable references. An expression $@x$ is a version of $x$ where all type class instance and disjointness arguments have been made explicit. (For the purposes of this paragraph, the type family $\mt{Top.folder}$ is a type class, though it isn't marked as one by the usual means.) An expression $@@x$ achieves the same effect, additionally making explicit all implicit constructor arguments. The default is that implicit arguments are inserted automatically after any reference to a variable, or after any application of a variable to one or more arguments. For such an expression, implicit wildcard arguments are added for the longest prefix of the expression's type consisting only of implicit polymorphism, type class instances, and disjointness obligations. The same syntax works for variables projected out of modules and for capitalized variables (datatype constructors).
adamc@529 550
adamc@852 551 At the expression level, an analogue is available of the composite $\lambda$ form for constructors. We define the language of binders as $b ::= p \mid [x] \mid [x \; ? \; \kappa] \mid X \mid [c \sim c]$. A lone variable $[x]$ stands for an implicit constructor variable of unspecified kind. The standard value-level function binder is recovered as the type-annotated pattern form $x : \tau$. It is a compile-time error to include a pattern $p$ that does not match every value of the appropriate type.
adamc@529 552
adamc@852 553 A local $\mt{val}$ declaration may bind a pattern instead of just a plain variable. As for function arguments, only irrefutable patterns are legal.
adamc@852 554
adamc@852 555 The keyword $\mt{fun}$ is a shorthand for $\mt{val} \; \mt{rec}$ that allows arguments to be specified before the equal sign in the definition of each mutually-recursive function, as in SML. Each curried argument must follow the grammar of the $b$ non-terminal introduced two paragraphs ago. A $\mt{fun}$ declaration is elaborated into a version that adds additional $\lambda$s to the fronts of the righthand sides, as appropriate.
adamc@529 556
adamc@529 557 A signature item $\mt{functor} \; X_1 \; (X_2 : S_1) : S_2$ is elaborated into $\mt{structure} \; X_1 : \mt{functor}(X_2 : S_1) : S_2$. A declaration $\mt{functor} \; X_1 \; (X_2 : S_1) : S_2 = M$ is elaborated into $\mt{structure} \; X_1 : \mt{functor}(X_2 : S_1) : S_2 = \mt{functor}(X_2 : S_1) : S_2 = M$.
adamc@529 558
adamc@852 559 An $\mt{open} \; \mt{constraints}$ declaration is implicitly inserted for the argument of every functor at the beginning of the functor body. For every declaration of the form $\mt{structure} \; X : S = \mt{struct} \ldots \mt{end}$, an $\mt{open} \; \mt{constraints} \; X$ declaration is implicitly inserted immediately afterward.
adamc@852 560
adamc@853 561 A declaration $\mt{table} \; x : \{(c = c,)^*\}$ is elaborated into $\mt{table} \; x : [(c = c,)^*]$.
adamc@529 562
adamc@529 563 The syntax $\mt{where} \; \mt{type}$ is an alternate form of $\mt{where} \; \mt{con}$.
adamc@529 564
adamc@529 565 The syntax $\mt{if} \; e \; \mt{then} \; e_1 \; \mt{else} \; e_2$ expands to $\mt{case} \; e \; \mt{of} \; \mt{Basis}.\mt{True} \Rightarrow e_1 \mid \mt{Basis}.\mt{False} \Rightarrow e_2$.
adamc@529 566
adamc@529 567 There are infix operator syntaxes for a number of functions defined in the $\mt{Basis}$ module. There is $=$ for $\mt{eq}$, $\neq$ for $\mt{neq}$, $-$ for $\mt{neg}$ (as a prefix operator) and $\mt{minus}$, $+$ for $\mt{plus}$, $\times$ for $\mt{times}$, $/$ for $\mt{div}$, $\%$ for $\mt{mod}$, $<$ for $\mt{lt}$, $\leq$ for $\mt{le}$, $>$ for $\mt{gt}$, and $\geq$ for $\mt{ge}$.
adamc@529 568
adamc@784 569 A signature item $\mt{table} \; x : c$ is shorthand for $\mt{val} \; x : \mt{Basis}.\mt{sql\_table} \; c \; []$. $\mt{view} \; x : c$ is shorthand for $\mt{val} \; x : \mt{Basis}.\mt{sql\_view} \; c$, $\mt{sequence} \; x$ is short for $\mt{val} \; x : \mt{Basis}.\mt{sql\_sequence}$. $\mt{cookie} \; x : \tau$ is shorthand for $\mt{val} \; x : \mt{Basis}.\mt{http\_cookie} \; \tau$, and $\mt{style} \; x$ is shorthand for $\mt{val} \; x : \mt{Basis}.\mt{css\_class}$.
adamc@529 570
adamc@530 571
adamc@530 572 \section{Static Semantics}
adamc@530 573
adamc@530 574 In this section, we give a declarative presentation of Ur's typing rules and related judgments. Inference is the subject of the next section; here, we assume that an oracle has filled in all wildcards with concrete values.
adamc@530 575
adamc@530 576 Since there is significant mutual recursion among the judgments, we introduce them all before beginning to give rules. We use the same variety of contexts throughout this section, implicitly introducing new sorts of context entries as needed.
adamc@530 577 \begin{itemize}
adamc@655 578 \item $\Gamma \vdash \kappa$ expresses kind well-formedness.
adamc@530 579 \item $\Gamma \vdash c :: \kappa$ assigns a kind to a constructor in a context.
adamc@530 580 \item $\Gamma \vdash c \sim c$ proves the disjointness of two record constructors; that is, that they share no field names. We overload the judgment to apply to pairs of field names as well.
adamc@531 581 \item $\Gamma \vdash c \hookrightarrow C$ proves that record constructor $c$ decomposes into set $C$ of field names and record constructors.
adamc@530 582 \item $\Gamma \vdash c \equiv c$ proves the computational equivalence of two constructors. This is often called a \emph{definitional equality} in the world of type theory.
adamc@530 583 \item $\Gamma \vdash e : \tau$ is a standard typing judgment.
adamc@534 584 \item $\Gamma \vdash p \leadsto \Gamma; \tau$ combines typing of patterns with calculation of which new variables they bind.
adamc@537 585 \item $\Gamma \vdash d \leadsto \Gamma$ expresses how a declaration modifies a context. We overload this judgment to apply to sequences of declarations, as well as to signature items and sequences of signature items.
adamc@537 586 \item $\Gamma \vdash S \equiv S$ is the signature equivalence judgment.
adamc@536 587 \item $\Gamma \vdash S \leq S$ is the signature compatibility judgment. We write $\Gamma \vdash S$ as shorthand for $\Gamma \vdash S \leq S$.
adamc@530 588 \item $\Gamma \vdash M : S$ is the module signature checking judgment.
adamc@537 589 \item $\mt{proj}(M, \overline{s}, V)$ is a partial function for projecting a signature item from $\overline{s}$, given the module $M$ that we project from. $V$ may be $\mt{con} \; x$, $\mt{datatype} \; x$, $\mt{val} \; x$, $\mt{signature} \; X$, or $\mt{structure} \; X$. The parameter $M$ is needed because the projected signature item may refer to other items from $\overline{s}$.
adamc@539 590 \item $\mt{selfify}(M, \overline{s})$ adds information to signature items $\overline{s}$ to reflect the fact that we are concerned with the particular module $M$. This function is overloaded to work over individual signature items as well.
adamc@530 591 \end{itemize}
adamc@530 592
adamc@655 593
adamc@655 594 \subsection{Kind Well-Formedness}
adamc@655 595
adamc@655 596 $$\infer{\Gamma \vdash \mt{Type}}{}
adamc@655 597 \quad \infer{\Gamma \vdash \mt{Unit}}{}
adamc@655 598 \quad \infer{\Gamma \vdash \mt{Name}}{}
adamc@655 599 \quad \infer{\Gamma \vdash \kappa_1 \to \kappa_2}{
adamc@655 600 \Gamma \vdash \kappa_1
adamc@655 601 & \Gamma \vdash \kappa_2
adamc@655 602 }
adamc@655 603 \quad \infer{\Gamma \vdash \{\kappa\}}{
adamc@655 604 \Gamma \vdash \kappa
adamc@655 605 }
adamc@655 606 \quad \infer{\Gamma \vdash (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@655 607 \forall i: \Gamma \vdash \kappa_i
adamc@655 608 }$$
adamc@655 609
adamc@655 610 $$\infer{\Gamma \vdash X}{
adamc@655 611 X \in \Gamma
adamc@655 612 }
adamc@655 613 \quad \infer{\Gamma \vdash X \longrightarrow \kappa}{
adamc@655 614 \Gamma, X \vdash \kappa
adamc@655 615 }$$
adamc@655 616
adamc@530 617 \subsection{Kinding}
adamc@530 618
adamc@655 619 We write $[X \mapsto \kappa_1]\kappa_2$ for capture-avoiding substitution of $\kappa_1$ for $X$ in $\kappa_2$.
adamc@655 620
adamc@530 621 $$\infer{\Gamma \vdash (c) :: \kappa :: \kappa}{
adamc@530 622 \Gamma \vdash c :: \kappa
adamc@530 623 }
adamc@530 624 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 625 x :: \kappa \in \Gamma
adamc@530 626 }
adamc@530 627 \quad \infer{\Gamma \vdash x :: \kappa}{
adamc@530 628 x :: \kappa = c \in \Gamma
adamc@530 629 }$$
adamc@530 630
adamc@530 631 $$\infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 632 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 633 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = \kappa
adamc@530 634 }
adamc@530 635 \quad \infer{\Gamma \vdash M.x :: \kappa}{
adamc@537 636 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 637 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@530 638 }$$
adamc@530 639
adamc@530 640 $$\infer{\Gamma \vdash \tau_1 \to \tau_2 :: \mt{Type}}{
adamc@530 641 \Gamma \vdash \tau_1 :: \mt{Type}
adamc@530 642 & \Gamma \vdash \tau_2 :: \mt{Type}
adamc@530 643 }
adamc@530 644 \quad \infer{\Gamma \vdash x \; ? \: \kappa \to \tau :: \mt{Type}}{
adamc@530 645 \Gamma, x :: \kappa \vdash \tau :: \mt{Type}
adamc@530 646 }
adamc@655 647 \quad \infer{\Gamma \vdash X \longrightarrow \tau :: \mt{Type}}{
adamc@655 648 \Gamma, X \vdash \tau :: \mt{Type}
adamc@655 649 }
adamc@530 650 \quad \infer{\Gamma \vdash \$c :: \mt{Type}}{
adamc@530 651 \Gamma \vdash c :: \{\mt{Type}\}
adamc@530 652 }$$
adamc@530 653
adamc@530 654 $$\infer{\Gamma \vdash c_1 \; c_2 :: \kappa_2}{
adamc@530 655 \Gamma \vdash c_1 :: \kappa_1 \to \kappa_2
adamc@530 656 & \Gamma \vdash c_2 :: \kappa_1
adamc@530 657 }
adamc@530 658 \quad \infer{\Gamma \vdash \lambda x \; :: \; \kappa_1 \Rightarrow c :: \kappa_1 \to \kappa_2}{
adamc@530 659 \Gamma, x :: \kappa_1 \vdash c :: \kappa_2
adamc@530 660 }$$
adamc@530 661
adamc@655 662 $$\infer{\Gamma \vdash c[\kappa'] :: [X \mapsto \kappa']\kappa}{
adamc@655 663 \Gamma \vdash c :: X \to \kappa
adamc@655 664 & \Gamma \vdash \kappa'
adamc@655 665 }
adamc@655 666 \quad \infer{\Gamma \vdash X \Longrightarrow c :: X \to \kappa}{
adamc@655 667 \Gamma, X \vdash c :: \kappa
adamc@655 668 }$$
adamc@655 669
adamc@530 670 $$\infer{\Gamma \vdash () :: \mt{Unit}}{}
adamc@530 671 \quad \infer{\Gamma \vdash \#X :: \mt{Name}}{}$$
adamc@530 672
adamc@530 673 $$\infer{\Gamma \vdash [\overline{c_i = c'_i}] :: \{\kappa\}}{
adamc@530 674 \forall i: \Gamma \vdash c_i : \mt{Name}
adamc@530 675 & \Gamma \vdash c'_i :: \kappa
adamc@530 676 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@530 677 }
adamc@530 678 \quad \infer{\Gamma \vdash c_1 \rc c_2 :: \{\kappa\}}{
adamc@530 679 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 680 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@530 681 & \Gamma \vdash c_1 \sim c_2
adamc@530 682 }$$
adamc@530 683
adamc@655 684 $$\infer{\Gamma \vdash \mt{map} :: (\kappa_1 \to \kappa_2) \to \{\kappa_1\} \to \{\kappa_2\}}{}$$
adamc@530 685
adamc@573 686 $$\infer{\Gamma \vdash (\overline c) :: (\kappa_1 \times \ldots \times \kappa_n)}{
adamc@573 687 \forall i: \Gamma \vdash c_i :: \kappa_i
adamc@530 688 }
adamc@573 689 \quad \infer{\Gamma \vdash c.i :: \kappa_i}{
adamc@573 690 \Gamma \vdash c :: (\kappa_1 \times \ldots \times \kappa_n)
adamc@530 691 }$$
adamc@530 692
adamc@655 693 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow \tau :: \mt{Type}}{
adamc@655 694 \Gamma \vdash c_1 :: \{\kappa\}
adamc@530 695 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@655 696 & \Gamma, c_1 \sim c_2 \vdash \tau :: \mt{Type}
adamc@530 697 }$$
adamc@530 698
adamc@531 699 \subsection{Record Disjointness}
adamc@531 700
adamc@531 701 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@558 702 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@558 703 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@558 704 & \forall c'_1 \in C_1, c'_2 \in C_2: \Gamma \vdash c'_1 \sim c'_2
adamc@531 705 }
adamc@531 706 \quad \infer{\Gamma \vdash X \sim X'}{
adamc@531 707 X \neq X'
adamc@531 708 }$$
adamc@531 709
adamc@531 710 $$\infer{\Gamma \vdash c_1 \sim c_2}{
adamc@531 711 c'_1 \sim c'_2 \in \Gamma
adamc@558 712 & \Gamma \vdash c'_1 \hookrightarrow C_1
adamc@558 713 & \Gamma \vdash c'_2 \hookrightarrow C_2
adamc@558 714 & c_1 \in C_1
adamc@558 715 & c_2 \in C_2
adamc@531 716 }$$
adamc@531 717
adamc@531 718 $$\infer{\Gamma \vdash c \hookrightarrow \{c\}}{}
adamc@531 719 \quad \infer{\Gamma \vdash [\overline{c = c'}] \hookrightarrow \{\overline{c}\}}{}
adamc@531 720 \quad \infer{\Gamma \vdash c_1 \rc c_2 \hookrightarrow C_1 \cup C_2}{
adamc@531 721 \Gamma \vdash c_1 \hookrightarrow C_1
adamc@531 722 & \Gamma \vdash c_2 \hookrightarrow C_2
adamc@531 723 }
adamc@531 724 \quad \infer{\Gamma \vdash c \hookrightarrow C}{
adamc@531 725 \Gamma \vdash c \equiv c'
adamc@531 726 & \Gamma \vdash c' \hookrightarrow C
adamc@531 727 }
adamc@531 728 \quad \infer{\Gamma \vdash \mt{map} \; f \; c \hookrightarrow C}{
adamc@531 729 \Gamma \vdash c \hookrightarrow C
adamc@531 730 }$$
adamc@531 731
adamc@541 732 \subsection{\label{definitional}Definitional Equality}
adamc@532 733
adamc@655 734 We use $\mathcal C$ to stand for a one-hole context that, when filled, yields a constructor. The notation $\mathcal C[c]$ plugs $c$ into $\mathcal C$. We omit the standard definition of one-hole contexts. We write $[x \mapsto c_1]c_2$ for capture-avoiding substitution of $c_1$ for $x$ in $c_2$, with analogous notation for substituting a kind in a constructor.
adamc@532 735
adamc@532 736 $$\infer{\Gamma \vdash c \equiv c}{}
adamc@532 737 \quad \infer{\Gamma \vdash c_1 \equiv c_2}{
adamc@532 738 \Gamma \vdash c_2 \equiv c_1
adamc@532 739 }
adamc@532 740 \quad \infer{\Gamma \vdash c_1 \equiv c_3}{
adamc@532 741 \Gamma \vdash c_1 \equiv c_2
adamc@532 742 & \Gamma \vdash c_2 \equiv c_3
adamc@532 743 }
adamc@532 744 \quad \infer{\Gamma \vdash \mathcal C[c_1] \equiv \mathcal C[c_2]}{
adamc@532 745 \Gamma \vdash c_1 \equiv c_2
adamc@532 746 }$$
adamc@532 747
adamc@532 748 $$\infer{\Gamma \vdash x \equiv c}{
adamc@532 749 x :: \kappa = c \in \Gamma
adamc@532 750 }
adamc@532 751 \quad \infer{\Gamma \vdash M.x \equiv c}{
adamc@537 752 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 753 & \mt{proj}(M, \overline{s}, \mt{con} \; x) = (\kappa, c)
adamc@532 754 }
adamc@532 755 \quad \infer{\Gamma \vdash (\overline c).i \equiv c_i}{}$$
adamc@532 756
adamc@532 757 $$\infer{\Gamma \vdash (\lambda x :: \kappa \Rightarrow c) \; c' \equiv [x \mapsto c'] c}{}
adamc@655 758 \quad \infer{\Gamma \vdash (X \Longrightarrow c) [\kappa] \equiv [X \mapsto \kappa] c}{}$$
adamc@655 759
adamc@655 760 $$\infer{\Gamma \vdash c_1 \rc c_2 \equiv c_2 \rc c_1}{}
adamc@532 761 \quad \infer{\Gamma \vdash c_1 \rc (c_2 \rc c_3) \equiv (c_1 \rc c_2) \rc c_3}{}$$
adamc@532 762
adamc@532 763 $$\infer{\Gamma \vdash [] \rc c \equiv c}{}
adamc@532 764 \quad \infer{\Gamma \vdash [\overline{c_1 = c'_1}] \rc [\overline{c_2 = c'_2}] \equiv [\overline{c_1 = c'_1}, \overline{c_2 = c'_2}]}{}$$
adamc@532 765
adamc@655 766 $$\infer{\Gamma \vdash \mt{map} \; f \; [] \equiv []}{}
adamc@655 767 \quad \infer{\Gamma \vdash \mt{map} \; f \; ([c_1 = c_2] \rc c) \equiv [c_1 = f \; c_2] \rc \mt{map} \; f \; c}{}$$
adamc@532 768
adamc@532 769 $$\infer{\Gamma \vdash \mt{map} \; (\lambda x \Rightarrow x) \; c \equiv c}{}
adamc@655 770 \quad \infer{\Gamma \vdash \mt{map} \; f \; (\mt{map} \; f' \; c)
adamc@655 771 \equiv \mt{map} \; (\lambda x \Rightarrow f \; (f' \; x)) \; c}{}$$
adamc@532 772
adamc@532 773 $$\infer{\Gamma \vdash \mt{map} \; f \; (c_1 \rc c_2) \equiv \mt{map} \; f \; c_1 \rc \mt{map} \; f \; c_2}{}$$
adamc@531 774
adamc@534 775 \subsection{Expression Typing}
adamc@533 776
adamc@873 777 We assume the existence of a function $T$ assigning types to literal constants. It maps integer constants to $\mt{Basis}.\mt{int}$, float constants to $\mt{Basis}.\mt{float}$, character constants to $\mt{Basis}.\mt{char}$, and string constants to $\mt{Basis}.\mt{string}$.
adamc@533 778
adamc@533 779 We also refer to a function $\mathcal I$, such that $\mathcal I(\tau)$ ``uses an oracle'' to instantiate all constructor function arguments at the beginning of $\tau$ that are marked implicit; i.e., replace $x_1 ::: \kappa_1 \to \ldots \to x_n ::: \kappa_n \to \tau$ with $[x_1 \mapsto c_1]\ldots[x_n \mapsto c_n]\tau$, where the $c_i$s are inferred and $\tau$ does not start like $x ::: \kappa \to \tau'$.
adamc@533 780
adamc@533 781 $$\infer{\Gamma \vdash e : \tau : \tau}{
adamc@533 782 \Gamma \vdash e : \tau
adamc@533 783 }
adamc@533 784 \quad \infer{\Gamma \vdash e : \tau}{
adamc@533 785 \Gamma \vdash e : \tau'
adamc@533 786 & \Gamma \vdash \tau' \equiv \tau
adamc@533 787 }
adamc@533 788 \quad \infer{\Gamma \vdash \ell : T(\ell)}{}$$
adamc@533 789
adamc@533 790 $$\infer{\Gamma \vdash x : \mathcal I(\tau)}{
adamc@533 791 x : \tau \in \Gamma
adamc@533 792 }
adamc@533 793 \quad \infer{\Gamma \vdash M.x : \mathcal I(\tau)}{
adamc@537 794 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 795 & \mt{proj}(M, \overline{s}, \mt{val} \; x) = \tau
adamc@533 796 }
adamc@533 797 \quad \infer{\Gamma \vdash X : \mathcal I(\tau)}{
adamc@533 798 X : \tau \in \Gamma
adamc@533 799 }
adamc@533 800 \quad \infer{\Gamma \vdash M.X : \mathcal I(\tau)}{
adamc@537 801 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 802 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \tau
adamc@533 803 }$$
adamc@533 804
adamc@533 805 $$\infer{\Gamma \vdash e_1 \; e_2 : \tau_2}{
adamc@533 806 \Gamma \vdash e_1 : \tau_1 \to \tau_2
adamc@533 807 & \Gamma \vdash e_2 : \tau_1
adamc@533 808 }
adamc@533 809 \quad \infer{\Gamma \vdash \lambda x : \tau_1 \Rightarrow e : \tau_1 \to \tau_2}{
adamc@533 810 \Gamma, x : \tau_1 \vdash e : \tau_2
adamc@533 811 }$$
adamc@533 812
adamc@533 813 $$\infer{\Gamma \vdash e [c] : [x \mapsto c]\tau}{
adamc@533 814 \Gamma \vdash e : x :: \kappa \to \tau
adamc@533 815 & \Gamma \vdash c :: \kappa
adamc@533 816 }
adamc@852 817 \quad \infer{\Gamma \vdash \lambda [x \; ? \; \kappa] \Rightarrow e : x \; ? \; \kappa \to \tau}{
adamc@533 818 \Gamma, x :: \kappa \vdash e : \tau
adamc@533 819 }$$
adamc@533 820
adamc@655 821 $$\infer{\Gamma \vdash e [\kappa] : [X \mapsto \kappa]\tau}{
adamc@655 822 \Gamma \vdash e : X \longrightarrow \tau
adamc@655 823 & \Gamma \vdash \kappa
adamc@655 824 }
adamc@655 825 \quad \infer{\Gamma \vdash X \Longrightarrow e : X \longrightarrow \tau}{
adamc@655 826 \Gamma, X \vdash e : \tau
adamc@655 827 }$$
adamc@655 828
adamc@533 829 $$\infer{\Gamma \vdash \{\overline{c = e}\} : \{\overline{c : \tau}\}}{
adamc@533 830 \forall i: \Gamma \vdash c_i :: \mt{Name}
adamc@533 831 & \Gamma \vdash e_i : \tau_i
adamc@533 832 & \forall i \neq j: \Gamma \vdash c_i \sim c_j
adamc@533 833 }
adamc@533 834 \quad \infer{\Gamma \vdash e.c : \tau}{
adamc@533 835 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 836 }
adamc@533 837 \quad \infer{\Gamma \vdash e_1 \rc e_2 : \$(c_1 \rc c_2)}{
adamc@533 838 \Gamma \vdash e_1 : \$c_1
adamc@533 839 & \Gamma \vdash e_2 : \$c_2
adamc@573 840 & \Gamma \vdash c_1 \sim c_2
adamc@533 841 }$$
adamc@533 842
adamc@533 843 $$\infer{\Gamma \vdash e \rcut c : \$c'}{
adamc@533 844 \Gamma \vdash e : \$([c = \tau] \rc c')
adamc@533 845 }
adamc@533 846 \quad \infer{\Gamma \vdash e \rcutM c : \$c'}{
adamc@533 847 \Gamma \vdash e : \$(c \rc c')
adamc@533 848 }$$
adamc@533 849
adamc@533 850 $$\infer{\Gamma \vdash \mt{let} \; \overline{ed} \; \mt{in} \; e \; \mt{end} : \tau}{
adamc@533 851 \Gamma \vdash \overline{ed} \leadsto \Gamma'
adamc@533 852 & \Gamma' \vdash e : \tau
adamc@533 853 }
adamc@533 854 \quad \infer{\Gamma \vdash \mt{case} \; e \; \mt{of} \; \overline{p \Rightarrow e} : \tau}{
adamc@533 855 \forall i: \Gamma \vdash p_i \leadsto \Gamma_i, \tau'
adamc@533 856 & \Gamma_i \vdash e_i : \tau
adamc@533 857 }$$
adamc@533 858
adamc@573 859 $$\infer{\Gamma \vdash \lambda [c_1 \sim c_2] \Rightarrow e : \lambda [c_1 \sim c_2] \Rightarrow \tau}{
adamc@533 860 \Gamma \vdash c_1 :: \{\kappa\}
adamc@655 861 & \Gamma \vdash c_2 :: \{\kappa'\}
adamc@533 862 & \Gamma, c_1 \sim c_2 \vdash e : \tau
adamc@662 863 }
adamc@662 864 \quad \infer{\Gamma \vdash e \; ! : \tau}{
adamc@662 865 \Gamma \vdash e : [c_1 \sim c_2] \Rightarrow \tau
adamc@662 866 & \Gamma \vdash c_1 \sim c_2
adamc@533 867 }$$
adamc@533 868
adamc@534 869 \subsection{Pattern Typing}
adamc@534 870
adamc@534 871 $$\infer{\Gamma \vdash \_ \leadsto \Gamma; \tau}{}
adamc@534 872 \quad \infer{\Gamma \vdash x \leadsto \Gamma, x : \tau; \tau}{}
adamc@534 873 \quad \infer{\Gamma \vdash \ell \leadsto \Gamma; T(\ell)}{}$$
adamc@534 874
adamc@534 875 $$\infer{\Gamma \vdash X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 876 X : \overline{x ::: \mt{Type}} \to \tau \in \Gamma
adamc@534 877 & \textrm{$\tau$ not a function type}
adamc@534 878 }
adamc@534 879 \quad \infer{\Gamma \vdash X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@534 880 X : \overline{x ::: \mt{Type}} \to \tau'' \to \tau \in \Gamma
adamc@534 881 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 882 }$$
adamc@534 883
adamc@534 884 $$\infer{\Gamma \vdash M.X \leadsto \Gamma; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 885 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 886 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau
adamc@534 887 & \textrm{$\tau$ not a function type}
adamc@534 888 }$$
adamc@534 889
adamc@534 890 $$\infer{\Gamma \vdash M.X \; p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau}{
adamc@537 891 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 892 & \mt{proj}(M, \overline{s}, \mt{val} \; X) = \overline{x ::: \mt{Type}} \to \tau'' \to \tau
adamc@534 893 & \Gamma \vdash p \leadsto \Gamma'; \overline{[x_i \mapsto \tau'_i]}\tau''
adamc@534 894 }$$
adamc@534 895
adamc@534 896 $$\infer{\Gamma \vdash \{\overline{x = p}\} \leadsto \Gamma_n; \{\overline{x = \tau}\}}{
adamc@534 897 \Gamma_0 = \Gamma
adamc@534 898 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 899 }
adamc@534 900 \quad \infer{\Gamma \vdash \{\overline{x = p}, \ldots\} \leadsto \Gamma_n; \$([\overline{x = \tau}] \rc c)}{
adamc@534 901 \Gamma_0 = \Gamma
adamc@534 902 & \forall i: \Gamma_i \vdash p_i \leadsto \Gamma_{i+1}; \tau_i
adamc@534 903 }$$
adamc@534 904
adamc@852 905 $$\infer{\Gamma \vdash p : \tau \leadsto \Gamma'; \tau}{
adamc@852 906 \Gamma \vdash p \leadsto \Gamma'; \tau'
adamc@852 907 & \Gamma \vdash \tau' \equiv \tau
adamc@852 908 }$$
adamc@852 909
adamc@535 910 \subsection{Declaration Typing}
adamc@535 911
adamc@535 912 We use an auxiliary judgment $\overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'$, expressing the enrichment of $\Gamma$ with the types of the datatype constructors $\overline{dc}$, when they are known to belong to datatype $x$ with type parameters $\overline{y}$.
adamc@535 913
adamc@655 914 This is the first judgment where we deal with constructor classes, for the $\mt{class}$ declaration form. We will omit their special handling in this formal specification. Section \ref{typeclasses} gives an informal description of how constructor classes influence type inference.
adamc@535 915
adamc@558 916 We presuppose the existence of a function $\mathcal O$, where $\mathcal O(M, \overline{s})$ implements the $\mt{open}$ declaration by producing a context with the appropriate entry for each available component of module $M$ with signature items $\overline{s}$. Where possible, $\mathcal O$ uses ``transparent'' entries (e.g., an abstract type $M.x$ is mapped to $x :: \mt{Type} = M.x$), so that the relationship with $M$ is maintained. A related function $\mathcal O_c$ builds a context containing the disjointness constraints found in $\overline s$.
adamc@537 917 We write $\kappa_1^n \to \kappa$ as a shorthand, where $\kappa_1^0 \to \kappa = \kappa$ and $\kappa_1^{n+1} \to \kappa_2 = \kappa_1 \to (\kappa_1^n \to \kappa_2)$. We write $\mt{len}(\overline{y})$ for the length of vector $\overline{y}$ of variables.
adamc@535 918
adamc@535 919 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 920 \quad \infer{\Gamma \vdash d, \overline{d} \leadsto \Gamma''}{
adamc@535 921 \Gamma \vdash d \leadsto \Gamma'
adamc@535 922 & \Gamma' \vdash \overline{d} \leadsto \Gamma''
adamc@535 923 }$$
adamc@535 924
adamc@535 925 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@535 926 \Gamma \vdash c :: \kappa
adamc@535 927 }
adamc@535 928 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@535 929 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@535 930 }$$
adamc@535 931
adamc@535 932 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 933 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 934 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@535 935 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@535 936 }$$
adamc@535 937
adamc@535 938 $$\infer{\Gamma \vdash \mt{val} \; x : \tau = e \leadsto \Gamma, x : \tau}{
adamc@535 939 \Gamma \vdash e : \tau
adamc@535 940 }$$
adamc@535 941
adamc@535 942 $$\infer{\Gamma \vdash \mt{val} \; \mt{rec} \; \overline{x : \tau = e} \leadsto \Gamma, \overline{x : \tau}}{
adamc@535 943 \forall i: \Gamma, \overline{x : \tau} \vdash e_i : \tau_i
adamc@535 944 & \textrm{$e_i$ starts with an expression $\lambda$, optionally preceded by constructor and disjointness $\lambda$s}
adamc@535 945 }$$
adamc@535 946
adamc@535 947 $$\infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : S}{
adamc@535 948 \Gamma \vdash M : S
adamc@558 949 & \textrm{ $M$ not a constant or application}
adamc@535 950 }
adamc@558 951 \quad \infer{\Gamma \vdash \mt{structure} \; X : S = M \leadsto \Gamma, X : \mt{selfify}(X, \overline{s})}{
adamc@558 952 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@539 953 }$$
adamc@539 954
adamc@539 955 $$\infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@535 956 \Gamma \vdash S
adamc@535 957 }$$
adamc@535 958
adamc@537 959 $$\infer{\Gamma \vdash \mt{open} \; M \leadsto \Gamma, \mathcal O(M, \overline{s})}{
adamc@537 960 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 961 }$$
adamc@535 962
adamc@535 963 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma}{
adamc@535 964 \Gamma \vdash c_1 :: \{\kappa\}
adamc@535 965 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@535 966 & \Gamma \vdash c_1 \sim c_2
adamc@535 967 }
adamc@537 968 \quad \infer{\Gamma \vdash \mt{open} \; \mt{constraints} \; M \leadsto \Gamma, \mathcal O_c(M, \overline{s})}{
adamc@537 969 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@535 970 }$$
adamc@535 971
adamc@784 972 $$\infer{\Gamma \vdash \mt{table} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_table} \; c \; []}{
adamc@535 973 \Gamma \vdash c :: \{\mt{Type}\}
adamc@535 974 }
adamc@784 975 \quad \infer{\Gamma \vdash \mt{view} \; x : c \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_view} \; c}{
adamc@784 976 \Gamma \vdash c :: \{\mt{Type}\}
adamc@784 977 }$$
adamc@784 978
adamc@784 979 $$\infer{\Gamma \vdash \mt{sequence} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{sql\_sequence}}{}$$
adamc@535 980
adamc@535 981 $$\infer{\Gamma \vdash \mt{cookie} \; x : \tau \leadsto \Gamma, x : \mt{Basis}.\mt{http\_cookie} \; \tau}{
adamc@535 982 \Gamma \vdash \tau :: \mt{Type}
adamc@784 983 }
adamc@784 984 \quad \infer{\Gamma \vdash \mt{style} \; x \leadsto \Gamma, x : \mt{Basis}.\mt{css\_class}}{}$$
adamc@535 985
adamc@1085 986 $$\infer{\Gamma \vdash \mt{task} \; e_1 = e_2 \leadsto \Gamma}{
adam@1348 987 \Gamma \vdash e_1 :: \mt{Basis}.\mt{task\_kind} \; \tau
adam@1348 988 & \Gamma \vdash e_2 :: \tau \to \mt{Basis}.\mt{transaction} \; \{\}
adamc@1085 989 }$$
adamc@1085 990
adamc@784 991 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 992 \Gamma \vdash c :: \kappa
adamc@535 993 }$$
adamc@535 994
adamc@535 995 $$\infer{\overline{y}; x; \Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@535 996 \quad \infer{\overline{y}; x; \Gamma \vdash X \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to x \; \overline{y}}{
adamc@535 997 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 998 }
adamc@535 999 \quad \infer{\overline{y}; x; \Gamma \vdash X \; \mt{of} \; \tau \mid \overline{dc} \leadsto \Gamma', X : \overline{y ::: \mt{Type}} \to \tau \to x \; \overline{y}}{
adamc@535 1000 \overline{y}; x; \Gamma \vdash \overline{dc} \leadsto \Gamma'
adamc@535 1001 }$$
adamc@535 1002
adamc@537 1003 \subsection{Signature Item Typing}
adamc@537 1004
adamc@537 1005 We appeal to a signature item analogue of the $\mathcal O$ function from the last subsection.
adamc@537 1006
adamc@537 1007 $$\infer{\Gamma \vdash \cdot \leadsto \Gamma}{}
adamc@537 1008 \quad \infer{\Gamma \vdash s, \overline{s} \leadsto \Gamma''}{
adamc@537 1009 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1010 & \Gamma' \vdash \overline{s} \leadsto \Gamma''
adamc@537 1011 }$$
adamc@537 1012
adamc@537 1013 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}
adamc@537 1014 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@537 1015 \Gamma \vdash c :: \kappa
adamc@537 1016 }
adamc@537 1017 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leadsto \Gamma'}{
adamc@537 1018 \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1019 }$$
adamc@537 1020
adamc@537 1021 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leadsto \Gamma'}{
adamc@537 1022 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1023 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1024 & \overline{y}; x; \Gamma, x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type} = M.z \vdash \overline{dc} \leadsto \Gamma'
adamc@537 1025 }$$
adamc@537 1026
adamc@537 1027 $$\infer{\Gamma \vdash \mt{val} \; x : \tau \leadsto \Gamma, x : \tau}{
adamc@537 1028 \Gamma \vdash \tau :: \mt{Type}
adamc@537 1029 }$$
adamc@537 1030
adamc@537 1031 $$\infer{\Gamma \vdash \mt{structure} \; X : S \leadsto \Gamma, X : S}{
adamc@537 1032 \Gamma \vdash S
adamc@537 1033 }
adamc@537 1034 \quad \infer{\Gamma \vdash \mt{signature} \; X = S \leadsto \Gamma, X = S}{
adamc@537 1035 \Gamma \vdash S
adamc@537 1036 }$$
adamc@537 1037
adamc@537 1038 $$\infer{\Gamma \vdash \mt{include} \; S \leadsto \Gamma, \mathcal O(\overline{s})}{
adamc@537 1039 \Gamma \vdash S
adamc@537 1040 & \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1041 }$$
adamc@537 1042
adamc@537 1043 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leadsto \Gamma, c_1 \sim c_2}{
adamc@537 1044 \Gamma \vdash c_1 :: \{\kappa\}
adamc@537 1045 & \Gamma \vdash c_2 :: \{\kappa\}
adamc@537 1046 }$$
adamc@537 1047
adamc@784 1048 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leadsto \Gamma, x :: \kappa = c}{
adamc@784 1049 \Gamma \vdash c :: \kappa
adamc@537 1050 }
adamc@784 1051 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa \leadsto \Gamma, x :: \kappa}{}$$
adamc@537 1052
adamc@536 1053 \subsection{Signature Compatibility}
adamc@536 1054
adamc@558 1055 To simplify the judgments in this section, we assume that all signatures are alpha-varied as necessary to avoid including multiple bindings for the same identifier. This is in addition to the usual alpha-variation of locally-bound variables.
adamc@537 1056
adamc@537 1057 We rely on a judgment $\Gamma \vdash \overline{s} \leq s'$, which expresses the occurrence in signature items $\overline{s}$ of an item compatible with $s'$. We also use a judgment $\Gamma \vdash \overline{dc} \leq \overline{dc}$, which expresses compatibility of datatype definitions.
adamc@537 1058
adamc@536 1059 $$\infer{\Gamma \vdash S \equiv S}{}
adamc@536 1060 \quad \infer{\Gamma \vdash S_1 \equiv S_2}{
adamc@536 1061 \Gamma \vdash S_2 \equiv S_1
adamc@536 1062 }
adamc@536 1063 \quad \infer{\Gamma \vdash X \equiv S}{
adamc@536 1064 X = S \in \Gamma
adamc@536 1065 }
adamc@536 1066 \quad \infer{\Gamma \vdash M.X \equiv S}{
adamc@537 1067 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1068 & \mt{proj}(M, \overline{s}, \mt{signature} \; X) = S
adamc@536 1069 }$$
adamc@536 1070
adamc@536 1071 $$\infer{\Gamma \vdash S \; \mt{where} \; \mt{con} \; x = c \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa = c \; \overline{s_2} \; \mt{end}}{
adamc@536 1072 \Gamma \vdash S \equiv \mt{sig} \; \overline{s^1} \; \mt{con} \; x :: \kappa \; \overline{s_2} \; \mt{end}
adamc@536 1073 & \Gamma \vdash c :: \kappa
adamc@537 1074 }
adamc@537 1075 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s^1} \; \mt{include} \; S \; \overline{s^2} \; \mt{end} \equiv \mt{sig} \; \overline{s^1} \; \overline{s} \; \overline{s^2} \; \mt{end}}{
adamc@537 1076 \Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}
adamc@536 1077 }$$
adamc@536 1078
adamc@536 1079 $$\infer{\Gamma \vdash S_1 \leq S_2}{
adamc@536 1080 \Gamma \vdash S_1 \equiv S_2
adamc@536 1081 }
adamc@536 1082 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \mt{end}}{}
adamc@537 1083 \quad \infer{\Gamma \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; s' \; \overline{s'} \; \mt{end}}{
adamc@537 1084 \Gamma \vdash \overline{s} \leq s'
adamc@537 1085 & \Gamma \vdash s' \leadsto \Gamma'
adamc@537 1086 & \Gamma' \vdash \mt{sig} \; \overline{s} \; \mt{end} \leq \mt{sig} \; \overline{s'} \; \mt{end}
adamc@537 1087 }$$
adamc@537 1088
adamc@537 1089 $$\infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1090 \Gamma \vdash s \leq s'
adamc@537 1091 }
adamc@537 1092 \quad \infer{\Gamma \vdash s \; \overline{s} \leq s'}{
adamc@537 1093 \Gamma \vdash s \leadsto \Gamma'
adamc@537 1094 & \Gamma' \vdash \overline{s} \leq s'
adamc@536 1095 }$$
adamc@536 1096
adamc@536 1097 $$\infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 \leq \mt{functor} (X : S'_1) : S'_2}{
adamc@536 1098 \Gamma \vdash S'_1 \leq S_1
adamc@536 1099 & \Gamma, X : S'_1 \vdash S_2 \leq S'_2
adamc@536 1100 }$$
adamc@536 1101
adamc@537 1102 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@537 1103 \quad \infer{\Gamma \vdash \mt{con} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}
adamc@558 1104 \quad \infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(\overline y)} \to \mt{Type}}{}$$
adamc@537 1105
adamc@537 1106 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{con} \; x :: \mt{Type}^{\mt{len}(y)} \to \mt{Type}}{
adamc@537 1107 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1108 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1109 }$$
adamc@537 1110
adamc@784 1111 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{con} \; x :: \kappa}{}
adamc@784 1112 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{con} \; x :: \kappa}{}$$
adamc@537 1113
adamc@537 1114 $$\infer{\Gamma \vdash \mt{con} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \mt{\kappa} = c_2}{
adamc@537 1115 \Gamma \vdash c_1 \equiv c_2
adamc@537 1116 }
adamc@784 1117 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{con} \; x :: \kappa = c_2}{
adamc@537 1118 \Gamma \vdash c_1 \equiv c_2
adamc@537 1119 }$$
adamc@537 1120
adamc@537 1121 $$\infer{\Gamma \vdash \mt{datatype} \; x \; \overline{y} = \overline{dc} \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1122 \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1123 }$$
adamc@537 1124
adamc@537 1125 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x \; \overline{y} = \overline{dc'}}{
adamc@537 1126 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@537 1127 & \mt{proj}(M, \overline{s}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})
adamc@537 1128 & \Gamma, \overline{y :: \mt{Type}} \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1129 }$$
adamc@537 1130
adamc@537 1131 $$\infer{\Gamma \vdash \cdot \leq \cdot}{}
adamc@537 1132 \quad \infer{\Gamma \vdash X; \overline{dc} \leq X; \overline{dc'}}{
adamc@537 1133 \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1134 }
adamc@537 1135 \quad \infer{\Gamma \vdash X \; \mt{of} \; \tau_1; \overline{dc} \leq X \; \mt{of} \; \tau_2; \overline{dc'}}{
adamc@537 1136 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1137 & \Gamma \vdash \overline{dc} \leq \overline{dc'}
adamc@537 1138 }$$
adamc@537 1139
adamc@537 1140 $$\infer{\Gamma \vdash \mt{datatype} \; x = \mt{datatype} \; M.z \leq \mt{datatype} \; x = \mt{datatype} \; M'.z'}{
adamc@537 1141 \Gamma \vdash M.z \equiv M'.z'
adamc@537 1142 }$$
adamc@537 1143
adamc@537 1144 $$\infer{\Gamma \vdash \mt{val} \; x : \tau_1 \leq \mt{val} \; x : \tau_2}{
adamc@537 1145 \Gamma \vdash \tau_1 \equiv \tau_2
adamc@537 1146 }
adamc@537 1147 \quad \infer{\Gamma \vdash \mt{structure} \; X : S_1 \leq \mt{structure} \; X : S_2}{
adamc@537 1148 \Gamma \vdash S_1 \leq S_2
adamc@537 1149 }
adamc@537 1150 \quad \infer{\Gamma \vdash \mt{signature} \; X = S_1 \leq \mt{signature} \; X = S_2}{
adamc@537 1151 \Gamma \vdash S_1 \leq S_2
adamc@537 1152 & \Gamma \vdash S_2 \leq S_1
adamc@537 1153 }$$
adamc@537 1154
adamc@537 1155 $$\infer{\Gamma \vdash \mt{constraint} \; c_1 \sim c_2 \leq \mt{constraint} \; c'_1 \sim c'_2}{
adamc@537 1156 \Gamma \vdash c_1 \equiv c'_1
adamc@537 1157 & \Gamma \vdash c_2 \equiv c'_2
adamc@537 1158 }$$
adamc@537 1159
adamc@655 1160 $$\infer{\Gamma \vdash \mt{class} \; x :: \kappa \leq \mt{class} \; x :: \kappa}{}
adamc@655 1161 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c \leq \mt{class} \; x :: \kappa}{}
adamc@655 1162 \quad \infer{\Gamma \vdash \mt{class} \; x :: \kappa = c_1 \leq \mt{class} \; x :: \kappa = c_2}{
adamc@537 1163 \Gamma \vdash c_1 \equiv c_2
adamc@537 1164 }$$
adamc@537 1165
adamc@538 1166 \subsection{Module Typing}
adamc@538 1167
adamc@538 1168 We use a helper function $\mt{sigOf}$, which converts declarations and sequences of declarations into their principal signature items and sequences of signature items, respectively.
adamc@538 1169
adamc@538 1170 $$\infer{\Gamma \vdash M : S}{
adamc@538 1171 \Gamma \vdash M : S'
adamc@538 1172 & \Gamma \vdash S' \leq S
adamc@538 1173 }
adamc@538 1174 \quad \infer{\Gamma \vdash \mt{struct} \; \overline{d} \; \mt{end} : \mt{sig} \; \mt{sigOf}(\overline{d}) \; \mt{end}}{
adamc@538 1175 \Gamma \vdash \overline{d} \leadsto \Gamma'
adamc@538 1176 }
adamc@538 1177 \quad \infer{\Gamma \vdash X : S}{
adamc@538 1178 X : S \in \Gamma
adamc@538 1179 }$$
adamc@538 1180
adamc@538 1181 $$\infer{\Gamma \vdash M.X : S}{
adamc@538 1182 \Gamma \vdash M : \mt{sig} \; \overline{s} \; \mt{end}
adamc@538 1183 & \mt{proj}(M, \overline{s}, \mt{structure} \; X) = S
adamc@538 1184 }$$
adamc@538 1185
adamc@538 1186 $$\infer{\Gamma \vdash M_1(M_2) : [X \mapsto M_2]S_2}{
adamc@538 1187 \Gamma \vdash M_1 : \mt{functor}(X : S_1) : S_2
adamc@538 1188 & \Gamma \vdash M_2 : S_1
adamc@538 1189 }
adamc@538 1190 \quad \infer{\Gamma \vdash \mt{functor} (X : S_1) : S_2 = M : \mt{functor} (X : S_1) : S_2}{
adamc@538 1191 \Gamma \vdash S_1
adamc@538 1192 & \Gamma, X : S_1 \vdash S_2
adamc@538 1193 & \Gamma, X : S_1 \vdash M : S_2
adamc@538 1194 }$$
adamc@538 1195
adamc@538 1196 \begin{eqnarray*}
adamc@538 1197 \mt{sigOf}(\cdot) &=& \cdot \\
adamc@538 1198 \mt{sigOf}(s \; \overline{s'}) &=& \mt{sigOf}(s) \; \mt{sigOf}(\overline{s'}) \\
adamc@538 1199 \\
adamc@538 1200 \mt{sigOf}(\mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@538 1201 \mt{sigOf}(\mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \overline{dc} \\
adamc@538 1202 \mt{sigOf}(\mt{datatype} \; x = \mt{datatype} \; M.z) &=& \mt{datatype} \; x = \mt{datatype} \; M.z \\
adamc@538 1203 \mt{sigOf}(\mt{val} \; x : \tau = e) &=& \mt{val} \; x : \tau \\
adamc@538 1204 \mt{sigOf}(\mt{val} \; \mt{rec} \; \overline{x : \tau = e}) &=& \overline{\mt{val} \; x : \tau} \\
adamc@538 1205 \mt{sigOf}(\mt{structure} \; X : S = M) &=& \mt{structure} \; X : S \\
adamc@538 1206 \mt{sigOf}(\mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@538 1207 \mt{sigOf}(\mt{open} \; M) &=& \mt{include} \; S \textrm{ (where $\Gamma \vdash M : S$)} \\
adamc@538 1208 \mt{sigOf}(\mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@538 1209 \mt{sigOf}(\mt{open} \; \mt{constraints} \; M) &=& \cdot \\
adamc@538 1210 \mt{sigOf}(\mt{table} \; x : c) &=& \mt{table} \; x : c \\
adamc@784 1211 \mt{sigOf}(\mt{view} \; x : c) &=& \mt{view} \; x : c \\
adamc@538 1212 \mt{sigOf}(\mt{sequence} \; x) &=& \mt{sequence} \; x \\
adamc@538 1213 \mt{sigOf}(\mt{cookie} \; x : \tau) &=& \mt{cookie} \; x : \tau \\
adamc@784 1214 \mt{sigOf}(\mt{style} \; x) &=& \mt{style} \; x \\
adamc@655 1215 \mt{sigOf}(\mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@538 1216 \end{eqnarray*}
adamc@539 1217 \begin{eqnarray*}
adamc@539 1218 \mt{selfify}(M, \cdot) &=& \cdot \\
adamc@558 1219 \mt{selfify}(M, s \; \overline{s'}) &=& \mt{selfify}(M, s) \; \mt{selfify}(M, \overline{s'}) \\
adamc@539 1220 \\
adamc@539 1221 \mt{selfify}(M, \mt{con} \; x :: \kappa) &=& \mt{con} \; x :: \kappa = M.x \\
adamc@539 1222 \mt{selfify}(M, \mt{con} \; x :: \kappa = c) &=& \mt{con} \; x :: \kappa = c \\
adamc@539 1223 \mt{selfify}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc}) &=& \mt{datatype} \; x \; \overline{y} = \mt{datatype} \; M.x \\
adamc@539 1224 \mt{selfify}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z) &=& \mt{datatype} \; x = \mt{datatype} \; M'.z \\
adamc@539 1225 \mt{selfify}(M, \mt{val} \; x : \tau) &=& \mt{val} \; x : \tau \\
adamc@539 1226 \mt{selfify}(M, \mt{structure} \; X : S) &=& \mt{structure} \; X : \mt{selfify}(M.X, \overline{s}) \textrm{ (where $\Gamma \vdash S \equiv \mt{sig} \; \overline{s} \; \mt{end}$)} \\
adamc@539 1227 \mt{selfify}(M, \mt{signature} \; X = S) &=& \mt{signature} \; X = S \\
adamc@539 1228 \mt{selfify}(M, \mt{include} \; S) &=& \mt{include} \; S \\
adamc@539 1229 \mt{selfify}(M, \mt{constraint} \; c_1 \sim c_2) &=& \mt{constraint} \; c_1 \sim c_2 \\
adamc@655 1230 \mt{selfify}(M, \mt{class} \; x :: \kappa) &=& \mt{class} \; x :: \kappa = M.x \\
adamc@655 1231 \mt{selfify}(M, \mt{class} \; x :: \kappa = c) &=& \mt{class} \; x :: \kappa = c \\
adamc@539 1232 \end{eqnarray*}
adamc@539 1233
adamc@540 1234 \subsection{Module Projection}
adamc@540 1235
adamc@540 1236 \begin{eqnarray*}
adamc@540 1237 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \\
adamc@540 1238 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa, c) \\
adamc@540 1239 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{con} \; x) &=& \mt{Type}^{\mt{len}(\overline{y})} \to \mt{Type} \\
adamc@540 1240 \mt{proj}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z \; \overline{s}, \mt{con} \; x) &=& (\mt{Type}^{\mt{len}(\overline{y})} \to \mt{Type}, M'.z) \textrm{ (where $\Gamma \vdash M' : \mt{sig} \; \overline{s'} \; \mt{end}$} \\
adamc@540 1241 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z) = (\overline{y}, \overline{dc})$)} \\
adamc@655 1242 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, \mt{con} \; x) &=& \kappa \to \mt{Type} \\
adamc@655 1243 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, \mt{con} \; x) &=& (\kappa \to \mt{Type}, c) \\
adamc@540 1244 \\
adamc@540 1245 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{datatype} \; x) &=& (\overline{y}, \overline{dc}) \\
adamc@540 1246 \mt{proj}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z \; \overline{s}, \mt{con} \; x) &=& \mt{proj}(M', \overline{s'}, \mt{datatype} \; z) \textrm{ (where $\Gamma \vdash M' : \mt{sig} \; \overline{s'} \; \mt{end}$)} \\
adamc@540 1247 \\
adamc@540 1248 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, \mt{val} \; x) &=& \tau \\
adamc@540 1249 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{val} \; X) &=& \overline{y ::: \mt{Type}} \to M.x \; \overline y \textrm{ (where $X \in \overline{dc}$)} \\
adamc@540 1250 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, \mt{val} \; X) &=& \overline{y ::: \mt{Type}} \to \tau \to M.x \; \overline y \textrm{ (where $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1251 \mt{proj}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z, \mt{val} \; X) &=& \overline{y ::: \mt{Type}} \to M.x \; \overline y \textrm{ (where $\Gamma \vdash M' : \mt{sig} \; \overline{s'} \; \mt{end}$} \\
adamc@540 1252 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \in \overline{dc}$)} \\
adamc@540 1253 \mt{proj}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z, \mt{val} \; X) &=& \overline{y ::: \mt{Type}} \to \tau \to M.x \; \overline y \textrm{ (where $\Gamma \vdash M' : \mt{sig} \; \overline{s'} \; \mt{end}$} \\
adamc@558 1254 && \textrm{and $\mt{proj}(M', \overline{s'}, \mt{datatype} \; z = (\overline{y}, \overline{dc})$ and $X \; \mt{of} \; \tau \in \overline{dc}$)} \\
adamc@540 1255 \\
adamc@540 1256 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, \mt{structure} \; X) &=& S \\
adamc@540 1257 \\
adamc@540 1258 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, \mt{signature} \; X) &=& S \\
adamc@540 1259 \\
adamc@540 1260 \mt{proj}(M, \mt{con} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1261 \mt{proj}(M, \mt{con} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1262 \mt{proj}(M, \mt{datatype} \; x \; \overline{y} = \overline{dc} \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1263 \mt{proj}(M, \mt{datatype} \; x = \mt{datatype} \; M'.z \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1264 \mt{proj}(M, \mt{val} \; x : \tau \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@540 1265 \mt{proj}(M, \mt{structure} \; X : S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1266 \mt{proj}(M, \mt{signature} \; X = S \; \overline{s}, V) &=& [X \mapsto M.X]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1267 \mt{proj}(M, \mt{include} \; S \; \overline{s}, V) &=& \mt{proj}(M, \overline{s'} \; \overline{s}, V) \textrm{ (where $\Gamma \vdash S \equiv \mt{sig} \; \overline{s'} \; \mt{end}$)} \\
adamc@540 1268 \mt{proj}(M, \mt{constraint} \; c_1 \sim c_2 \; \overline{s}, V) &=& \mt{proj}(M, \overline{s}, V) \\
adamc@655 1269 \mt{proj}(M, \mt{class} \; x :: \kappa \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@655 1270 \mt{proj}(M, \mt{class} \; x :: \kappa = c \; \overline{s}, V) &=& [x \mapsto M.x]\mt{proj}(M, \overline{s}, V) \\
adamc@540 1271 \end{eqnarray*}
adamc@540 1272
adamc@541 1273
adamc@541 1274 \section{Type Inference}
adamc@541 1275
adamc@541 1276 The Ur/Web compiler uses \emph{heuristic type inference}, with no claims of completeness with respect to the declarative specification of the last section. The rules in use seem to work well in practice. This section summarizes those rules, to help Ur programmers predict what will work and what won't.
adamc@541 1277
adamc@541 1278 \subsection{Basic Unification}
adamc@541 1279
adamc@560 1280 Type-checkers for languages based on the Hindley-Milner type discipline, like ML and Haskell, take advantage of \emph{principal typing} properties, making complete type inference relatively straightforward. Inference algorithms are traditionally implemented using type unification variables, at various points asserting equalities between types, in the process discovering the values of type variables. The Ur/Web compiler uses the same basic strategy, but the complexity of the type system rules out easy completeness.
adamc@541 1281
adamc@656 1282 Type-checking can require evaluating recursive functional programs, thanks to the type-level $\mt{map}$ operator. When a unification variable appears in such a type, the next step of computation can be undetermined. The value of that variable might be determined later, but this would be ``too late'' for the unification problems generated at the first occurrence. This is the essential source of incompleteness.
adamc@541 1283
adamc@541 1284 Nonetheless, the unification engine tends to do reasonably well. Unlike in ML, polymorphism is never inferred in definitions; it must be indicated explicitly by writing out constructor-level parameters. By writing these and other annotations, the programmer can generally get the type inference engine to do most of the type reconstruction work.
adamc@541 1285
adamc@541 1286 \subsection{Unifying Record Types}
adamc@541 1287
adamc@570 1288 The type inference engine tries to take advantage of the algebraic rules governing type-level records, as shown in Section \ref{definitional}. When two constructors of record kind are unified, they are reduced to normal forms, with like terms crossed off from each normal form until, hopefully, nothing remains. This cannot be complete, with the inclusion of unification variables. The type-checker can help you understand what goes wrong when the process fails, as it outputs the unmatched remainders of the two normal forms.
adamc@541 1289
adamc@656 1290 \subsection{\label{typeclasses}Constructor Classes}
adamc@541 1291
adamc@784 1292 Ur includes a constructor class facility inspired by Haskell's. The current version is experimental, with very general Prolog-like facilities that can lead to compile-time non-termination.
adamc@541 1293
adamc@784 1294 Constructor classes are integrated with the module system. A constructor class of kind $\kappa$ is just a constructor of kind $\kappa$. By marking such a constructor $c$ as a constructor class, the programmer instructs the type inference engine to, in each scope, record all values of types $c \; c_1 \; \ldots \; c_n$ as \emph{instances}. Any function argument whose type is of such a form is treated as implicit, to be determined by examining the current instance database.
adamc@541 1295
adamc@656 1296 The ``dictionary encoding'' often used in Haskell implementations is made explicit in Ur. Constructor class instances are just properly-typed values, and they can also be considered as ``proofs'' of membership in the class. In some cases, it is useful to pass these proofs around explicitly. An underscore written where a proof is expected will also be inferred, if possible, from the current instance database.
adamc@541 1297
adamc@656 1298 Just as for constructors, constructors classes may be exported from modules, and they may be exported as concrete or abstract. Concrete constructor classes have their ``real'' definitions exposed, so that client code may add new instances freely. Abstract constructor classes are useful as ``predicates'' that can be used to enforce invariants, as we will see in some definitions of SQL syntax in the Ur/Web standard library.
adamc@541 1299
adamc@541 1300 \subsection{Reverse-Engineering Record Types}
adamc@541 1301
adamc@656 1302 It's useful to write Ur functions and functors that take record constructors as inputs, but these constructors can grow quite long, even though their values are often implied by other arguments. The compiler uses a simple heuristic to infer the values of unification variables that are mapped over, yielding known results. If the result is empty, we're done; if it's not empty, we replace a single unification variable with a new constructor formed from three new unification variables, as in $[\alpha = \beta] \rc \gamma$. This process can often be repeated to determine a unification variable fully.
adamc@541 1303
adamc@541 1304 \subsection{Implicit Arguments in Functor Applications}
adamc@541 1305
adamc@656 1306 Constructor, constraint, and constructor class witness members of structures may be omitted, when those structures are used in contexts where their assigned signatures imply how to fill in those missing members. This feature combines well with reverse-engineering to allow for uses of complicated meta-programming functors with little more code than would be necessary to invoke an untyped, ad-hoc code generator.
adamc@541 1307
adamc@541 1308
adamc@542 1309 \section{The Ur Standard Library}
adamc@542 1310
adamc@542 1311 The built-in parts of the Ur/Web standard library are described by the signature in \texttt{lib/basis.urs} in the distribution. A module $\mt{Basis}$ ascribing to that signature is available in the initial environment, and every program is implicitly prefixed by $\mt{open} \; \mt{Basis}$.
adamc@542 1312
adamc@542 1313 Additionally, other common functions that are definable within Ur are included in \texttt{lib/top.urs} and \texttt{lib/top.ur}. This $\mt{Top}$ module is also opened implicitly.
adamc@542 1314
adamc@542 1315 The idea behind Ur is to serve as the ideal host for embedded domain-specific languages. For now, however, the ``generic'' functionality is intermixed with Ur/Web-specific functionality, including in these two library modules. We hope that these generic library components have types that speak for themselves. The next section introduces the Ur/Web-specific elements. Here, we only give the type declarations from the beginning of $\mt{Basis}$.
adamc@542 1316 $$\begin{array}{l}
adamc@542 1317 \mt{type} \; \mt{int} \\
adamc@542 1318 \mt{type} \; \mt{float} \\
adamc@873 1319 \mt{type} \; \mt{char} \\
adamc@542 1320 \mt{type} \; \mt{string} \\
adamc@542 1321 \mt{type} \; \mt{time} \\
adamc@785 1322 \mt{type} \; \mt{blob} \\
adamc@542 1323 \\
adamc@542 1324 \mt{type} \; \mt{unit} = \{\} \\
adamc@542 1325 \\
adamc@542 1326 \mt{datatype} \; \mt{bool} = \mt{False} \mid \mt{True} \\
adamc@542 1327 \\
adamc@785 1328 \mt{datatype} \; \mt{option} \; \mt{t} = \mt{None} \mid \mt{Some} \; \mt{of} \; \mt{t} \\
adamc@785 1329 \\
adamc@785 1330 \mt{datatype} \; \mt{list} \; \mt{t} = \mt{Nil} \mid \mt{Cons} \; \mt{of} \; \mt{t} \times \mt{list} \; \mt{t}
adamc@542 1331 \end{array}$$
adamc@542 1332
adamc@1123 1333 The only unusual element of this list is the $\mt{blob}$ type, which stands for binary sequences. Simple blobs can be created from strings via $\mt{Basis.textBlob}$. Blobs will also be generated from HTTP file uploads.
adamc@785 1334
adam@1297 1335 Ur also supports \emph{polymorphic variants}, a dual to extensible records that has been popularized by OCaml. A type $\mt{variant} \; r$ represents an $n$-ary sum type, with one constructor for each field of record $r$. Each constructor $c$ takes an argument of type $r.c$; the type $\{\}$ can be used to ``simulate'' a nullary constructor. The \cd{make} function builds a variant value, while \cd{match} implements pattern-matching, with match cases represented as records of functions.
adam@1297 1336 $$\begin{array}{l}
adam@1297 1337 \mt{con} \; \mt{variant} :: \{\mt{Type}\} \to \mt{Type} \\
adam@1297 1338 \mt{val} \; \mt{make} : \mt{nm} :: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{ts} ::: \{\mt{Type}\} \to [[\mt{nm}] \sim \mt{ts}] \Rightarrow \mt{t} \to \mt{variant} \; ([\mt{nm} = \mt{t}] \rc \mt{ts}) \\
adam@1297 1339 \mt{val} \; \mt{match} : \mt{ts} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{variant} \; \mt{ts} \to \$(\mt{map} \; (\lambda \mt{t'} \Rightarrow \mt{t'} \to \mt{t}) \; \mt{ts}) \to \mt{t}
adam@1297 1340 \end{array}$$
adam@1297 1341
adamc@657 1342 Another important generic Ur element comes at the beginning of \texttt{top.urs}.
adamc@657 1343
adamc@657 1344 $$\begin{array}{l}
adamc@657 1345 \mt{con} \; \mt{folder} :: \mt{K} \longrightarrow \{\mt{K}\} \to \mt{Type} \\
adamc@657 1346 \\
adamc@657 1347 \mt{val} \; \mt{fold} : \mt{K} \longrightarrow \mt{tf} :: (\{\mt{K}\} \to \mt{Type}) \\
adamc@657 1348 \hspace{.1in} \to (\mt{nm} :: \mt{Name} \to \mt{v} :: \mt{K} \to \mt{r} :: \{\mt{K}\} \to [[\mt{nm}] \sim \mt{r}] \Rightarrow \\
adamc@657 1349 \hspace{.2in} \mt{tf} \; \mt{r} \to \mt{tf} \; ([\mt{nm} = \mt{v}] \rc \mt{r})) \\
adamc@657 1350 \hspace{.1in} \to \mt{tf} \; [] \\
adamc@657 1351 \hspace{.1in} \to \mt{r} :: \{\mt{K}\} \to \mt{folder} \; \mt{r} \to \mt{tf} \; \mt{r}
adamc@657 1352 \end{array}$$
adamc@657 1353
adamc@657 1354 For a type-level record $\mt{r}$, a $\mt{folder} \; \mt{r}$ encodes a permutation of $\mt{r}$'s elements. The $\mt{fold}$ function can be called on a $\mt{folder}$ to iterate over the elements of $\mt{r}$ in that order. $\mt{fold}$ is parameterized on a type-level function to be used to calculate the type of each intermediate result of folding. After processing a subset $\mt{r'}$ of $\mt{r}$'s entries, the type of the accumulator should be $\mt{tf} \; \mt{r'}$. The next two expression arguments to $\mt{fold}$ are the usual step function and initial accumulator, familiar from fold functions over lists. The final two arguments are the record to fold over and a $\mt{folder}$ for it.
adamc@657 1355
adamc@664 1356 The Ur compiler treats $\mt{folder}$ like a constructor class, using built-in rules to infer $\mt{folder}$s for records with known structure. The order in which field names are mentioned in source code is used as a hint about the permutation that the programmer would like.
adamc@657 1357
adamc@542 1358
adamc@542 1359 \section{The Ur/Web Standard Library}
adamc@542 1360
adam@1400 1361 Some operations are only allowed in server-side code or only in client-side code. The type system does not enforce such restrictions, but the compiler enforces them in the process of whole-program compilation. In the discussion below, we note when a set of operations has a location restriction.
adam@1400 1362
adamc@658 1363 \subsection{Monads}
adamc@658 1364
adamc@658 1365 The Ur Basis defines the monad constructor class from Haskell.
adamc@658 1366
adamc@658 1367 $$\begin{array}{l}
adamc@658 1368 \mt{class} \; \mt{monad} :: \mt{Type} \to \mt{Type} \\
adamc@658 1369 \mt{val} \; \mt{return} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t} ::: \mt{Type} \\
adamc@658 1370 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1371 \hspace{.1in} \to \mt{t} \to \mt{m} \; \mt{t} \\
adamc@658 1372 \mt{val} \; \mt{bind} : \mt{m} ::: (\mt{Type} \to \mt{Type}) \to \mt{t1} ::: \mt{Type} \to \mt{t2} ::: \mt{Type} \\
adamc@658 1373 \hspace{.1in} \to \mt{monad} \; \mt{m} \\
adamc@658 1374 \hspace{.1in} \to \mt{m} \; \mt{t1} \to (\mt{t1} \to \mt{m} \; \mt{t2}) \\
adamc@658 1375 \hspace{.1in} \to \mt{m} \; \mt{t2}
adamc@658 1376 \end{array}$$
adamc@658 1377
adamc@542 1378 \subsection{Transactions}
adamc@542 1379
adamc@542 1380 Ur is a pure language; we use Haskell's trick to support controlled side effects. The standard library defines a monad $\mt{transaction}$, meant to stand for actions that may be undone cleanly. By design, no other kinds of actions are supported.
adamc@542 1381 $$\begin{array}{l}
adamc@542 1382 \mt{con} \; \mt{transaction} :: \mt{Type} \to \mt{Type} \\
adamc@658 1383 \mt{val} \; \mt{transaction\_monad} : \mt{monad} \; \mt{transaction}
adamc@542 1384 \end{array}$$
adamc@542 1385
adamc@1123 1386 For debugging purposes, a transactional function is provided for outputting a string on the server process' \texttt{stderr}.
adamc@1123 1387 $$\begin{array}{l}
adamc@1123 1388 \mt{val} \; \mt{debug} : \mt{string} \to \mt{transaction} \; \mt{unit}
adamc@1123 1389 \end{array}$$
adamc@1123 1390
adamc@542 1391 \subsection{HTTP}
adamc@542 1392
adam@1400 1393 There are transactions for reading an HTTP header by name and for getting and setting strongly-typed cookies. Cookies may only be created by the $\mt{cookie}$ declaration form, ensuring that they be named consistently based on module structure. For now, cookie operations are server-side only.
adamc@542 1394 $$\begin{array}{l}
adamc@786 1395 \mt{con} \; \mt{http\_cookie} :: \mt{Type} \to \mt{Type} \\
adamc@786 1396 \mt{val} \; \mt{getCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; (\mt{option} \; \mt{t}) \\
adamc@1050 1397 \mt{val} \; \mt{setCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \{\mt{Value} : \mt{t}, \mt{Expires} : \mt{option} \; \mt{time}, \mt{Secure} : \mt{bool}\} \to \mt{transaction} \; \mt{unit} \\
adamc@1050 1398 \mt{val} \; \mt{clearCookie} : \mt{t} ::: \mt{Type} \to \mt{http\_cookie} \; \mt{t} \to \mt{transaction} \; \mt{unit}
adamc@786 1399 \end{array}$$
adamc@786 1400
adamc@786 1401 There are also an abstract $\mt{url}$ type and functions for converting to it, based on the policy defined by \texttt{[allow|deny] url} directives in the project file.
adamc@786 1402 $$\begin{array}{l}
adamc@786 1403 \mt{type} \; \mt{url} \\
adamc@786 1404 \mt{val} \; \mt{bless} : \mt{string} \to \mt{url} \\
adamc@786 1405 \mt{val} \; \mt{checkUrl} : \mt{string} \to \mt{option} \; \mt{url}
adamc@786 1406 \end{array}$$
adamc@786 1407 $\mt{bless}$ raises a runtime error if the string passed to it fails the URL policy.
adamc@786 1408
adam@1400 1409 It is possible to grab the current page's URL or to build a URL for an arbitrary transaction that would also be an acceptable value of a \texttt{link} attribute of the \texttt{a} tag. These are server-side operations.
adamc@1085 1410 $$\begin{array}{l}
adamc@1085 1411 \mt{val} \; \mt{currentUrl} : \mt{transaction} \; \mt{url} \\
adamc@1085 1412 \mt{val} \; \mt{url} : \mt{transaction} \; \mt{page} \to \mt{url}
adamc@1085 1413 \end{array}$$
adamc@1085 1414
adamc@1085 1415 Page generation may be interrupted at any time with a request to redirect to a particular URL instead.
adamc@1085 1416 $$\begin{array}{l}
adamc@1085 1417 \mt{val} \; \mt{redirect} : \mt{t} ::: \mt{Type} \to \mt{url} \to \mt{transaction} \; \mt{t}
adamc@1085 1418 \end{array}$$
adamc@1085 1419
adam@1400 1420 It's possible for pages to return files of arbitrary MIME types. A file can be input from the user using this data type, along with the $\mt{upload}$ form tag. These functions and those described in the following paragraph are server-side.
adamc@786 1421 $$\begin{array}{l}
adamc@786 1422 \mt{type} \; \mt{file} \\
adamc@786 1423 \mt{val} \; \mt{fileName} : \mt{file} \to \mt{option} \; \mt{string} \\
adamc@786 1424 \mt{val} \; \mt{fileMimeType} : \mt{file} \to \mt{string} \\
adamc@786 1425 \mt{val} \; \mt{fileData} : \mt{file} \to \mt{blob}
adamc@786 1426 \end{array}$$
adamc@786 1427
adam@1465 1428 It is also possible to get HTTP request headers and set HTTP response headers, using abstract types similar to the one for URLs.
adam@1465 1429
adam@1465 1430 $$\begin{array}{l}
adam@1465 1431 \mt{type} \; \mt{requestHeader} \\
adam@1465 1432 \mt{val} \; \mt{blessRequestHeader} : \mt{string} \to \mt{requestHeader} \\
adam@1465 1433 \mt{val} \; \mt{checkRequestHeader} : \mt{string} \to \mt{option} \; \mt{requestHeader} \\
adam@1465 1434 \mt{val} \; \mt{getHeader} : \mt{requestHeader} \to \mt{transaction} \; (\mt{option} \; \mt{string}) \\
adam@1465 1435 \\
adam@1465 1436 \mt{type} \; \mt{responseHeader} \\
adam@1465 1437 \mt{val} \; \mt{blessResponseHeader} : \mt{string} \to \mt{responseHeader} \\
adam@1465 1438 \mt{val} \; \mt{checkResponseHeader} : \mt{string} \to \mt{option} \; \mt{responseHeader} \\
adam@1465 1439 \mt{val} \; \mt{setHeader} : \mt{responseHeader} \to \mt{string} \to \mt{transaction} \; \mt{unit}
adam@1465 1440 \end{array}$$
adam@1465 1441
adamc@786 1442 A blob can be extracted from a file and returned as the page result. There are bless and check functions for MIME types analogous to those for URLs.
adamc@786 1443 $$\begin{array}{l}
adamc@786 1444 \mt{type} \; \mt{mimeType} \\
adamc@786 1445 \mt{val} \; \mt{blessMime} : \mt{string} \to \mt{mimeType} \\
adamc@786 1446 \mt{val} \; \mt{checkMime} : \mt{string} \to \mt{option} \; \mt{mimeType} \\
adamc@786 1447 \mt{val} \; \mt{returnBlob} : \mt{t} ::: \mt{Type} \to \mt{blob} \to \mt{mimeType} \to \mt{transaction} \; \mt{t}
adamc@542 1448 \end{array}$$
adamc@542 1449
adamc@543 1450 \subsection{SQL}
adamc@543 1451
adam@1400 1452 Everything about SQL database access is restricted to server-side code.
adam@1400 1453
adamc@543 1454 The fundamental unit of interest in the embedding of SQL is tables, described by a type family and creatable only via the $\mt{table}$ declaration form.
adamc@543 1455 $$\begin{array}{l}
adamc@785 1456 \mt{con} \; \mt{sql\_table} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1457 \end{array}$$
adamc@785 1458 The first argument to this constructor gives the names and types of a table's columns, and the second argument gives the set of valid keys. Keys are the only subsets of the columns that may be referenced as foreign keys. Each key has a name.
adamc@785 1459
adamc@785 1460 We also have the simpler type family of SQL views, which have no keys.
adamc@785 1461 $$\begin{array}{l}
adamc@785 1462 \mt{con} \; \mt{sql\_view} :: \{\mt{Type}\} \to \mt{Type}
adamc@543 1463 \end{array}$$
adamc@543 1464
adamc@785 1465 A multi-parameter type class is used to allow tables and views to be used interchangeably, with a way of extracting the set of columns from each.
adamc@785 1466 $$\begin{array}{l}
adamc@785 1467 \mt{class} \; \mt{fieldsOf} :: \mt{Type} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1468 \mt{val} \; \mt{fieldsOf\_table} : \mt{fs} ::: \{\mt{Type}\} \to \mt{keys} ::: \{\{\mt{Unit}\}\} \to \mt{fieldsOf} \; (\mt{sql\_table} \; \mt{fs} \; \mt{keys}) \; \mt{fs} \\
adamc@785 1469 \mt{val} \; \mt{fieldsOf\_view} : \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; (\mt{sql\_view} \; \mt{fs}) \; \mt{fs}
adamc@785 1470 \end{array}$$
adamc@785 1471
adamc@785 1472 \subsubsection{Table Constraints}
adamc@785 1473
adamc@785 1474 Tables may be declared with constraints, such that database modifications that violate the constraints are blocked. A table may have at most one \texttt{PRIMARY KEY} constraint, which gives the subset of columns that will most often be used to look up individual rows in the table.
adamc@785 1475
adamc@785 1476 $$\begin{array}{l}
adamc@785 1477 \mt{con} \; \mt{primary\_key} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type} \\
adamc@785 1478 \mt{val} \; \mt{no\_primary\_key} : \mt{fs} ::: \{\mt{Type}\} \to \mt{primary\_key} \; \mt{fs} \; [] \\
adamc@785 1479 \mt{val} \; \mt{primary\_key} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{key1} :: \mt{Name} \to \mt{keys} :: \{\mt{Type}\} \\
adamc@785 1480 \hspace{.1in} \to [[\mt{key1}] \sim \mt{keys}] \Rightarrow [[\mt{key1} = \mt{t}] \rc \mt{keys} \sim \mt{rest}] \\
adamc@785 1481 \hspace{.1in} \Rightarrow \$([\mt{key1} = \mt{sql\_injectable\_prim} \; \mt{t}] \rc \mt{map} \; \mt{sql\_injectable\_prim} \; \mt{keys}) \\
adamc@785 1482 \hspace{.1in} \to \mt{primary\_key} \; ([\mt{key1} = \mt{t}] \rc \mt{keys} \rc \mt{rest}) \; [\mt{Pkey} = [\mt{key1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{keys}]
adamc@785 1483 \end{array}$$
adamc@785 1484 The type class $\mt{sql\_injectable\_prim}$ characterizes which types are allowed in SQL and are not $\mt{option}$ types. In SQL, a \texttt{PRIMARY KEY} constraint enforces after-the-fact that a column may not contain \texttt{NULL}s, but Ur/Web forces that information to be included in table types from the beginning. Thus, the only effect of this kind of constraint in Ur/Web is to enforce uniqueness of the given key within the table.
adamc@785 1485
adamc@785 1486 A type family stands for sets of named constraints of the remaining varieties.
adamc@785 1487 $$\begin{array}{l}
adamc@785 1488 \mt{con} \; \mt{sql\_constraints} :: \{\mt{Type}\} \to \{\{\mt{Unit}\}\} \to \mt{Type}
adamc@785 1489 \end{array}$$
adamc@785 1490 The first argument gives the column types of the table being constrained, and the second argument maps constraint names to the keys that they define. Constraints that don't define keys are mapped to ``empty keys.''
adamc@785 1491
adamc@785 1492 There is a type family of individual, unnamed constraints.
adamc@785 1493 $$\begin{array}{l}
adamc@785 1494 \mt{con} \; \mt{sql\_constraint} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \mt{Type}
adamc@785 1495 \end{array}$$
adamc@785 1496 The first argument is the same as above, and the second argument gives the key columns for just this constraint.
adamc@785 1497
adamc@785 1498 We have operations for assembling constraints into constraint sets.
adamc@785 1499 $$\begin{array}{l}
adamc@785 1500 \mt{val} \; \mt{no\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_constraints} \; \mt{fs} \; [] \\
adamc@785 1501 \mt{val} \; \mt{one\_constraint} : \mt{fs} ::: \{\mt{Type}\} \to \mt{unique} ::: \{\mt{Unit}\} \to \mt{name} :: \mt{Name} \\
adamc@785 1502 \hspace{.1in} \to \mt{sql\_constraint} \; \mt{fs} \; \mt{unique} \to \mt{sql\_constraints} \; \mt{fs} \; [\mt{name} = \mt{unique}] \\
adamc@785 1503 \mt{val} \; \mt{join\_constraints} : \mt{fs} ::: \{\mt{Type}\} \to \mt{uniques1} ::: \{\{\mt{Unit}\}\} \to \mt{uniques2} ::: \{\{\mt{Unit}\}\} \to [\mt{uniques1} \sim \mt{uniques2}] \\
adamc@785 1504 \hspace{.1in} \Rightarrow \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques1} \to \mt{sql\_constraints} \; \mt{fs} \; \mt{uniques2} \to \mt{sql\_constraints} \; \mt{fs} \; (\mt{uniques1} \rc \mt{uniques2})
adamc@785 1505 \end{array}$$
adamc@785 1506
adamc@785 1507 A \texttt{UNIQUE} constraint forces a set of columns to be a key, which means that no combination of column values may occur more than once in the table. The $\mt{unique1}$ and $\mt{unique}$ arguments are separated out only to ensure that empty \texttt{UNIQUE} constraints are rejected.
adamc@785 1508 $$\begin{array}{l}
adamc@785 1509 \mt{val} \; \mt{unique} : \mt{rest} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{unique1} :: \mt{Name} \to \mt{unique} :: \{\mt{Type}\} \\
adamc@785 1510 \hspace{.1in} \to [[\mt{unique1}] \sim \mt{unique}] \Rightarrow [[\mt{unique1} = \mt{t}] \rc \mt{unique} \sim \mt{rest}] \\
adamc@785 1511 \hspace{.1in} \Rightarrow \mt{sql\_constraint} \; ([\mt{unique1} = \mt{t}] \rc \mt{unique} \rc \mt{rest}) \; ([\mt{unique1}] \rc \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{unique})
adamc@785 1512 \end{array}$$
adamc@785 1513
adamc@785 1514 A \texttt{FOREIGN KEY} constraint connects a set of local columns to a local or remote key, enforcing that the local columns always reference an existent row of the foreign key's table. A local column of type $\mt{t}$ may be linked to a foreign column of type $\mt{option} \; \mt{t}$, and vice versa. We formalize that notion with a type class.
adamc@785 1515 $$\begin{array}{l}
adamc@785 1516 \mt{class} \; \mt{linkable} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@785 1517 \mt{val} \; \mt{linkable\_same} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; \mt{t} \\
adamc@785 1518 \mt{val} \; \mt{linkable\_from\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; (\mt{option} \; \mt{t}) \; \mt{t} \\
adamc@785 1519 \mt{val} \; \mt{linkable\_to\_nullable} : \mt{t} ::: \mt{Type} \to \mt{linkable} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@785 1520 \end{array}$$
adamc@785 1521
adamc@785 1522 The $\mt{matching}$ type family uses $\mt{linkable}$ to define when two keys match up type-wise.
adamc@785 1523 $$\begin{array}{l}
adamc@785 1524 \mt{con} \; \mt{matching} :: \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1525 \mt{val} \; \mt{mat\_nil} : \mt{matching} \; [] \; [] \\
adamc@785 1526 \mt{val} \; \mt{mat\_cons} : \mt{t1} ::: \mt{Type} \to \mt{rest1} ::: \{\mt{Type}\} \to \mt{t2} ::: \mt{Type} \to \mt{rest2} ::: \{\mt{Type}\} \to \mt{nm1} :: \mt{Name} \to \mt{nm2} :: \mt{Name} \\
adamc@785 1527 \hspace{.1in} \to [[\mt{nm1}] \sim \mt{rest1}] \Rightarrow [[\mt{nm2}] \sim \mt{rest2}] \Rightarrow \mt{linkable} \; \mt{t1} \; \mt{t2} \to \mt{matching} \; \mt{rest1} \; \mt{rest2} \\
adamc@785 1528 \hspace{.1in} \to \mt{matching} \; ([\mt{nm1} = \mt{t1}] \rc \mt{rest1}) \; ([\mt{nm2} = \mt{t2}] \rc \mt{rest2})
adamc@785 1529 \end{array}$$
adamc@785 1530
adamc@785 1531 SQL provides a number of different propagation modes for \texttt{FOREIGN KEY} constraints, governing what happens when a row containing a still-referenced foreign key value is deleted or modified to have a different key value. The argument of a propagation mode's type gives the local key type.
adamc@785 1532 $$\begin{array}{l}
adamc@785 1533 \mt{con} \; \mt{propagation\_mode} :: \{\mt{Type}\} \to \mt{Type} \\
adamc@785 1534 \mt{val} \; \mt{restrict} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1535 \mt{val} \; \mt{cascade} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1536 \mt{val} \; \mt{no\_action} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; \mt{fs} \\
adamc@785 1537 \mt{val} \; \mt{set\_null} : \mt{fs} ::: \{\mt{Type}\} \to \mt{propagation\_mode} \; (\mt{map} \; \mt{option} \; \mt{fs})
adamc@785 1538 \end{array}$$
adamc@785 1539
adamc@785 1540 Finally, we put these ingredient together to define the \texttt{FOREIGN KEY} constraint function.
adamc@785 1541 $$\begin{array}{l}
adamc@785 1542 \mt{val} \; \mt{foreign\_key} : \mt{mine1} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{mine} ::: \{\mt{Type}\} \to \mt{munused} ::: \{\mt{Type}\} \to \mt{foreign} ::: \{\mt{Type}\} \\
adamc@785 1543 \hspace{.1in} \to \mt{funused} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{uniques} ::: \{\{\mt{Unit}\}\} \\
adamc@785 1544 \hspace{.1in} \to [[\mt{mine1}] \sim \mt{mine}] \Rightarrow [[\mt{mine1} = \mt{t}] \rc \mt{mine} \sim \mt{munused}] \Rightarrow [\mt{foreign} \sim \mt{funused}] \Rightarrow [[\mt{nm}] \sim \mt{uniques}] \\
adamc@785 1545 \hspace{.1in} \Rightarrow \mt{matching} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}) \; \mt{foreign} \\
adamc@785 1546 \hspace{.1in} \to \mt{sql\_table} \; (\mt{foreign} \rc \mt{funused}) \; ([\mt{nm} = \mt{map} \; (\lambda \_ \Rightarrow ()) \; \mt{foreign}] \rc \mt{uniques}) \\
adamc@785 1547 \hspace{.1in} \to \{\mt{OnDelete} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine}), \\
adamc@785 1548 \hspace{.2in} \mt{OnUpdate} : \mt{propagation\_mode} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine})\} \\
adamc@785 1549 \hspace{.1in} \to \mt{sql\_constraint} \; ([\mt{mine1} = \mt{t}] \rc \mt{mine} \rc \mt{munused}) \; []
adamc@785 1550 \end{array}$$
adamc@785 1551
adamc@785 1552 The last kind of constraint is a \texttt{CHECK} constraint, which attaches a boolean invariant over a row's contents. It is defined using the $\mt{sql\_exp}$ type family, which we discuss in more detail below.
adamc@785 1553 $$\begin{array}{l}
adamc@785 1554 \mt{val} \; \mt{check} : \mt{fs} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; [] \; [] \; \mt{fs} \; \mt{bool} \to \mt{sql\_constraint} \; \mt{fs} \; []
adamc@785 1555 \end{array}$$
adamc@785 1556
adamc@785 1557 Section \ref{tables} shows the expanded syntax of the $\mt{table}$ declaration and signature item that includes constraints. There is no other way to use constraints with SQL in Ur/Web.
adamc@785 1558
adamc@784 1559
adamc@543 1560 \subsubsection{Queries}
adamc@543 1561
adam@1400 1562 A final query is constructed via the $\mt{sql\_query}$ function. Constructor arguments respectively specify the unrestricted free table variables (which will only be available in subqueries), the free table variables that may only be mentioned within arguments to aggregate functions, table fields we select (as records mapping tables to the subsets of their fields that we choose), and the (always named) extra expressions that we select.
adamc@543 1563 $$\begin{array}{l}
adam@1400 1564 \mt{con} \; \mt{sql\_query} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@1193 1565 \mt{val} \; \mt{sql\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1566 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1567 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1568 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1569 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1193 1570 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adam@1400 1571 \hspace{.1in} \Rightarrow \{\mt{Rows} : \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}, \\
adamc@1193 1572 \hspace{.2in} \mt{OrderBy} : \mt{sql\_order\_by} \; (\mt{free} \rc \mt{tables}) \; \mt{selectedExps}, \\
adamc@543 1573 \hspace{.2in} \mt{Limit} : \mt{sql\_limit}, \\
adamc@543 1574 \hspace{.2in} \mt{Offset} : \mt{sql\_offset}\} \\
adam@1400 1575 \hspace{.1in} \to \mt{sql\_query} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1576 \end{array}$$
adamc@543 1577
adamc@545 1578 Queries are used by folding over their results inside transactions.
adamc@545 1579 $$\begin{array}{l}
adam@1400 1580 \mt{val} \; \mt{query} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to [\mt{tables} \sim \mt{exps}] \Rightarrow \mt{state} ::: \mt{Type} \to \mt{sql\_query} \; [] \; [] \; \mt{tables} \; \mt{exps} \\
adamc@658 1581 \hspace{.1in} \to (\$(\mt{exps} \rc \mt{map} \; (\lambda \mt{fields} :: \{\mt{Type}\} \Rightarrow \$\mt{fields}) \; \mt{tables}) \\
adamc@545 1582 \hspace{.2in} \to \mt{state} \to \mt{transaction} \; \mt{state}) \\
adamc@545 1583 \hspace{.1in} \to \mt{state} \to \mt{transaction} \; \mt{state}
adamc@545 1584 \end{array}$$
adamc@545 1585
adam@1400 1586 Most of the complexity of the query encoding is in the type $\mt{sql\_query1}$, which includes simple queries and derived queries based on relational operators. Constructor arguments respectively specify the unrestricted free table veriables, the aggregate-only free table variables, the tables we select from, the subset of fields that we keep from each table for the result rows, and the extra expressions that we select.
adamc@543 1587 $$\begin{array}{l}
adam@1400 1588 \mt{con} \; \mt{sql\_query1} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@543 1589 \\
adamc@543 1590 \mt{type} \; \mt{sql\_relop} \\
adamc@543 1591 \mt{val} \; \mt{sql\_union} : \mt{sql\_relop} \\
adamc@543 1592 \mt{val} \; \mt{sql\_intersect} : \mt{sql\_relop} \\
adamc@543 1593 \mt{val} \; \mt{sql\_except} : \mt{sql\_relop} \\
adam@1400 1594 \mt{val} \; \mt{sql\_relop} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1595 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adam@1400 1596 \hspace{.1in} \to \mt{tables1} ::: \{\{\mt{Type}\}\} \\
adamc@543 1597 \hspace{.1in} \to \mt{tables2} ::: \{\{\mt{Type}\}\} \\
adamc@543 1598 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1599 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@543 1600 \hspace{.1in} \to \mt{sql\_relop} \\
adam@1458 1601 \hspace{.1in} \to \mt{bool} \; (* \; \mt{ALL} \; *) \\
adam@1400 1602 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables1} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1603 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables2} \; \mt{selectedFields} \; \mt{selectedExps} \\
adam@1400 1604 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{selectedFields} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1605 \end{array}$$
adamc@543 1606
adamc@543 1607 $$\begin{array}{l}
adamc@1193 1608 \mt{val} \; \mt{sql\_query1} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adam@1400 1609 \hspace{.1in} \to \mt{afree} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1610 \hspace{.1in} \to \mt{tables} ::: \{\{\mt{Type}\}\} \\
adamc@543 1611 \hspace{.1in} \to \mt{grouped} ::: \{\{\mt{Type}\}\} \\
adamc@543 1612 \hspace{.1in} \to \mt{selectedFields} ::: \{\{\mt{Type}\}\} \\
adamc@543 1613 \hspace{.1in} \to \mt{selectedExps} ::: \{\mt{Type}\} \\
adamc@1085 1614 \hspace{.1in} \to \mt{empties} :: \{\mt{Unit}\} \\
adamc@1193 1615 \hspace{.1in} \to [\mt{free} \sim \mt{tables}] \\
adamc@1193 1616 \hspace{.1in} \Rightarrow [\mt{free} \sim \mt{grouped}] \\
adam@1400 1617 \hspace{.1in} \Rightarrow [\mt{afree} \sim \mt{tables}] \\
adamc@1193 1618 \hspace{.1in} \Rightarrow [\mt{empties} \sim \mt{selectedFields}] \\
adamc@1085 1619 \hspace{.1in} \Rightarrow \{\mt{Distinct} : \mt{bool}, \\
adamc@1193 1620 \hspace{.2in} \mt{From} : \mt{sql\_from\_items} \; \mt{free} \; \mt{tables}, \\
adam@1400 1621 \hspace{.2in} \mt{Where} : \mt{sql\_exp} \; (\mt{free} \rc \mt{tables}) \; \mt{afree} \; [] \; \mt{bool}, \\
adamc@543 1622 \hspace{.2in} \mt{GroupBy} : \mt{sql\_subset} \; \mt{tables} \; \mt{grouped}, \\
adam@1400 1623 \hspace{.2in} \mt{Having} : \mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; [] \; \mt{bool}, \\
adamc@1085 1624 \hspace{.2in} \mt{SelectFields} : \mt{sql\_subset} \; \mt{grouped} \; (\mt{map} \; (\lambda \_ \Rightarrow []) \; \mt{empties} \rc \mt{selectedFields}), \\
adam@1400 1625 \hspace{.2in} \mt {SelectExps} : \$(\mt{map} \; (\mt{sql\_exp} \; (\mt{free} \rc \mt{grouped}) \; (\mt{afree} \rc \mt{tables}) \; []) \; \mt{selectedExps}) \} \\
adam@1400 1626 \hspace{.1in} \to \mt{sql\_query1} \; \mt{free} \; \mt{afree} \; \mt{tables} \; \mt{selectedFields} \; \mt{selectedExps}
adamc@543 1627 \end{array}$$
adamc@543 1628
adamc@543 1629 To encode projection of subsets of fields in $\mt{SELECT}$ clauses, and to encode $\mt{GROUP} \; \mt{BY}$ clauses, we rely on a type family $\mt{sql\_subset}$, capturing what it means for one record of table fields to be a subset of another. The main constructor $\mt{sql\_subset}$ ``proves subset facts'' by requiring a split of a record into kept and dropped parts. The extra constructor $\mt{sql\_subset\_all}$ is a convenience for keeping all fields of a record.
adamc@543 1630 $$\begin{array}{l}
adamc@543 1631 \mt{con} \; \mt{sql\_subset} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@543 1632 \mt{val} \; \mt{sql\_subset} : \mt{keep\_drop} :: \{(\{\mt{Type}\} \times \{\mt{Type}\})\} \\
adamc@543 1633 \hspace{.1in} \to \mt{sql\_subset} \\
adamc@658 1634 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1 \rc \mt{fields}.2)\; \mt{keep\_drop}) \\
adamc@658 1635 \hspace{.2in} (\mt{map} \; (\lambda \mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\}) \Rightarrow \mt{fields}.1) \; \mt{keep\_drop}) \\
adamc@543 1636 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables}
adamc@543 1637 \end{array}$$
adamc@543 1638
adamc@560 1639 SQL expressions are used in several places, including $\mt{SELECT}$, $\mt{WHERE}$, $\mt{HAVING}$, and $\mt{ORDER} \; \mt{BY}$ clauses. They reify a fragment of the standard SQL expression language, while making it possible to inject ``native'' Ur values in some places. The arguments to the $\mt{sql\_exp}$ type family respectively give the unrestricted-availability table fields, the table fields that may only be used in arguments to aggregate functions, the available selected expressions, and the type of the expression.
adamc@543 1640 $$\begin{array}{l}
adamc@543 1641 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type}
adamc@543 1642 \end{array}$$
adamc@543 1643
adamc@543 1644 Any field in scope may be converted to an expression.
adamc@543 1645 $$\begin{array}{l}
adamc@543 1646 \mt{val} \; \mt{sql\_field} : \mt{otherTabs} ::: \{\{\mt{Type}\}\} \to \mt{otherFields} ::: \{\mt{Type}\} \\
adamc@543 1647 \hspace{.1in} \to \mt{fieldType} ::: \mt{Type} \to \mt{agg} ::: \{\{\mt{Type}\}\} \\
adamc@543 1648 \hspace{.1in} \to \mt{exps} ::: \{\mt{Type}\} \\
adamc@543 1649 \hspace{.1in} \to \mt{tab} :: \mt{Name} \to \mt{field} :: \mt{Name} \\
adamc@543 1650 \hspace{.1in} \to \mt{sql\_exp} \; ([\mt{tab} = [\mt{field} = \mt{fieldType}] \rc \mt{otherFields}] \rc \mt{otherTabs}) \; \mt{agg} \; \mt{exps} \; \mt{fieldType}
adamc@543 1651 \end{array}$$
adamc@543 1652
adamc@544 1653 There is an analogous function for referencing named expressions.
adamc@544 1654 $$\begin{array}{l}
adamc@544 1655 \mt{val} \; \mt{sql\_exp} : \mt{tabs} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{t} ::: \mt{Type} \to \mt{rest} ::: \{\mt{Type}\} \to \mt{nm} :: \mt{Name} \\
adamc@544 1656 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tabs} \; \mt{agg} \; ([\mt{nm} = \mt{t}] \rc \mt{rest}) \; \mt{t}
adamc@544 1657 \end{array}$$
adamc@544 1658
adamc@544 1659 Ur values of appropriate types may be injected into SQL expressions.
adamc@544 1660 $$\begin{array}{l}
adamc@786 1661 \mt{class} \; \mt{sql\_injectable\_prim} \\
adamc@786 1662 \mt{val} \; \mt{sql\_bool} : \mt{sql\_injectable\_prim} \; \mt{bool} \\
adamc@786 1663 \mt{val} \; \mt{sql\_int} : \mt{sql\_injectable\_prim} \; \mt{int} \\
adamc@786 1664 \mt{val} \; \mt{sql\_float} : \mt{sql\_injectable\_prim} \; \mt{float} \\
adamc@786 1665 \mt{val} \; \mt{sql\_string} : \mt{sql\_injectable\_prim} \; \mt{string} \\
adamc@786 1666 \mt{val} \; \mt{sql\_time} : \mt{sql\_injectable\_prim} \; \mt{time} \\
adamc@786 1667 \mt{val} \; \mt{sql\_blob} : \mt{sql\_injectable\_prim} \; \mt{blob} \\
adamc@786 1668 \mt{val} \; \mt{sql\_channel} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{channel} \; \mt{t}) \\
adamc@786 1669 \mt{val} \; \mt{sql\_client} : \mt{sql\_injectable\_prim} \; \mt{client} \\
adamc@786 1670 \\
adamc@544 1671 \mt{class} \; \mt{sql\_injectable} \\
adamc@786 1672 \mt{val} \; \mt{sql\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@786 1673 \mt{val} \; \mt{sql\_option\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{sql\_injectable} \; (\mt{option} \; \mt{t}) \\
adamc@786 1674 \\
adamc@544 1675 \mt{val} \; \mt{sql\_inject} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \to \mt{sql\_injectable} \; \mt{t} \\
adamc@544 1676 \hspace{.1in} \to \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t}
adamc@544 1677 \end{array}$$
adamc@544 1678
adamc@1123 1679 Additionally, most function-free types may be injected safely, via the $\mt{serialized}$ type family.
adamc@1123 1680 $$\begin{array}{l}
adamc@1123 1681 \mt{con} \; \mt{serialized} :: \mt{Type} \to \mt{Type} \\
adamc@1123 1682 \mt{val} \; \mt{serialize} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{serialized} \; \mt{t} \\
adamc@1123 1683 \mt{val} \; \mt{deserialize} : \mt{t} ::: \mt{Type} \to \mt{serialized} \; \mt{t} \to \mt{t} \\
adamc@1123 1684 \mt{val} \; \mt{sql\_serialized} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; (\mt{serialized} \; \mt{t})
adamc@1123 1685 \end{array}$$
adamc@1123 1686
adamc@544 1687 We have the SQL nullness test, which is necessary because of the strange SQL semantics of equality in the presence of null values.
adamc@544 1688 $$\begin{array}{l}
adamc@544 1689 \mt{val} \; \mt{sql\_is\_null} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1690 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; (\mt{option} \; \mt{t}) \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{bool}
adamc@544 1691 \end{array}$$
adamc@544 1692
adamc@559 1693 We have generic nullary, unary, and binary operators.
adamc@544 1694 $$\begin{array}{l}
adamc@544 1695 \mt{con} \; \mt{sql\_nfunc} :: \mt{Type} \to \mt{Type} \\
adamc@544 1696 \mt{val} \; \mt{sql\_current\_timestamp} : \mt{sql\_nfunc} \; \mt{time} \\
adamc@544 1697 \mt{val} \; \mt{sql\_nfunc} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1698 \hspace{.1in} \to \mt{sql\_nfunc} \; \mt{t} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{t} \\\end{array}$$
adamc@544 1699
adamc@544 1700 $$\begin{array}{l}
adamc@544 1701 \mt{con} \; \mt{sql\_unary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1702 \mt{val} \; \mt{sql\_not} : \mt{sql\_unary} \; \mt{bool} \; \mt{bool} \\
adamc@544 1703 \mt{val} \; \mt{sql\_unary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1704 \hspace{.1in} \to \mt{sql\_unary} \; \mt{arg} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res} \\
adamc@544 1705 \end{array}$$
adamc@544 1706
adamc@544 1707 $$\begin{array}{l}
adamc@544 1708 \mt{con} \; \mt{sql\_binary} :: \mt{Type} \to \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@544 1709 \mt{val} \; \mt{sql\_and} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1710 \mt{val} \; \mt{sql\_or} : \mt{sql\_binary} \; \mt{bool} \; \mt{bool} \; \mt{bool} \\
adamc@544 1711 \mt{val} \; \mt{sql\_binary} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{arg_1} ::: \mt{Type} \to \mt{arg_2} ::: \mt{Type} \to \mt{res} ::: \mt{Type} \\
adamc@544 1712 \hspace{.1in} \to \mt{sql\_binary} \; \mt{arg_1} \; \mt{arg_2} \; \mt{res} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_1} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{arg_2} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{res}
adamc@544 1713 \end{array}$$
adamc@544 1714
adamc@544 1715 $$\begin{array}{l}
adamc@559 1716 \mt{class} \; \mt{sql\_arith} \\
adamc@559 1717 \mt{val} \; \mt{sql\_int\_arith} : \mt{sql\_arith} \; \mt{int} \\
adamc@559 1718 \mt{val} \; \mt{sql\_float\_arith} : \mt{sql\_arith} \; \mt{float} \\
adamc@559 1719 \mt{val} \; \mt{sql\_neg} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_unary} \; \mt{t} \; \mt{t} \\
adamc@559 1720 \mt{val} \; \mt{sql\_plus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1721 \mt{val} \; \mt{sql\_minus} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1722 \mt{val} \; \mt{sql\_times} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1723 \mt{val} \; \mt{sql\_div} : \mt{t} ::: \mt{Type} \to \mt{sql\_arith} \; \mt{t} \to \mt{sql\_binary} \; \mt{t} \; \mt{t} \; \mt{t} \\
adamc@559 1724 \mt{val} \; \mt{sql\_mod} : \mt{sql\_binary} \; \mt{int} \; \mt{int} \; \mt{int}
adamc@559 1725 \end{array}$$
adamc@544 1726
adamc@656 1727 Finally, we have aggregate functions. The $\mt{COUNT(\ast)}$ syntax is handled specially, since it takes no real argument. The other aggregate functions are placed into a general type family, using constructor classes to restrict usage to properly-typed arguments. The key aspect of the $\mt{sql\_aggregate}$ function's type is the shift of aggregate-function-only fields into unrestricted fields.
adamc@544 1728 $$\begin{array}{l}
adamc@544 1729 \mt{val} \; \mt{sql\_count} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{int}
adamc@544 1730 \end{array}$$
adamc@544 1731
adamc@544 1732 $$\begin{array}{l}
adamc@1188 1733 \mt{con} \; \mt{sql\_aggregate} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@1188 1734 \mt{val} \; \mt{sql\_aggregate} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{dom} ::: \mt{Type} \to \mt{ran} ::: \mt{Type} \\
adamc@1188 1735 \hspace{.1in} \to \mt{sql\_aggregate} \; \mt{dom} \; \mt{ran} \to \mt{sql\_exp} \; \mt{agg} \; \mt{agg} \; \mt{exps} \; \mt{dom} \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{ran}
adamc@1188 1736 \end{array}$$
adamc@1188 1737
adamc@1188 1738 $$\begin{array}{l}
adamc@1188 1739 \mt{val} \; \mt{sql\_count\_col} : \mt{t} ::: \mt{Type} \to \mt{sql\_aggregate} \; (\mt{option} \; \mt{t}) \; \mt{int}
adamc@544 1740 \end{array}$$
adam@1400 1741
adam@1400 1742 Most aggregate functions are typed using a two-parameter constructor class $\mt{nullify}$ which maps $\mt{option}$ types to themselves and adds $\mt{option}$ to others. That is, this constructor class represents the process of making an SQL type ``nullable.''
adamc@544 1743
adamc@544 1744 $$\begin{array}{l}
adamc@544 1745 \mt{class} \; \mt{sql\_summable} \\
adamc@544 1746 \mt{val} \; \mt{sql\_summable\_int} : \mt{sql\_summable} \; \mt{int} \\
adamc@544 1747 \mt{val} \; \mt{sql\_summable\_float} : \mt{sql\_summable} \; \mt{float} \\
adam@1400 1748 \mt{val} \; \mt{sql\_avg} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400 1749 \mt{val} \; \mt{sql\_sum} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_summable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1750 \end{array}$$
adamc@544 1751
adamc@544 1752 $$\begin{array}{l}
adamc@544 1753 \mt{class} \; \mt{sql\_maxable} \\
adamc@544 1754 \mt{val} \; \mt{sql\_maxable\_int} : \mt{sql\_maxable} \; \mt{int} \\
adamc@544 1755 \mt{val} \; \mt{sql\_maxable\_float} : \mt{sql\_maxable} \; \mt{float} \\
adamc@544 1756 \mt{val} \; \mt{sql\_maxable\_string} : \mt{sql\_maxable} \; \mt{string} \\
adamc@544 1757 \mt{val} \; \mt{sql\_maxable\_time} : \mt{sql\_maxable} \; \mt{time} \\
adam@1400 1758 \mt{val} \; \mt{sql\_max} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt} \\
adam@1400 1759 \mt{val} \; \mt{sql\_min} : \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \to \mt{sql\_maxable} \; \mt{t} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_aggregate} \; \mt{t} \; \mt{nt}
adamc@544 1760 \end{array}$$
adamc@544 1761
adamc@1193 1762 Any SQL query that returns single columns may be turned into a subquery expression.
adamc@1193 1763
adamc@786 1764 $$\begin{array}{l}
adam@1421 1765 \mt{val} \; \mt{sql\_subquery} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{agg} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{nm} ::: \mt{Name} \to \mt{t} ::: \mt{Type} \to \mt{nt} ::: \mt{Type} \\
adam@1421 1766 \hspace{.1in} \to \mt{nullify} \; \mt{t} \; \mt{nt} \to \mt{sql\_query} \; \mt{tables} \; \mt{agg} \; [\mt{nm} = \mt{t}] \to \mt{sql\_exp} \; \mt{tables} \; \mt{agg} \; \mt{exps} \; \mt{nt}
adamc@1193 1767 \end{array}$$
adamc@1193 1768
adamc@1193 1769 \texttt{FROM} clauses are specified using a type family, whose arguments are the free table variables and the table variables bound by this clause.
adamc@1193 1770 $$\begin{array}{l}
adamc@1193 1771 \mt{con} \; \mt{sql\_from\_items} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \mt{Type} \\
adamc@1193 1772 \mt{val} \; \mt{sql\_from\_table} : \mt{free} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1773 \hspace{.1in} \to \mt{t} ::: \mt{Type} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{fieldsOf} \; \mt{t} \; \mt{fs} \to \mt{name} :: \mt{Name} \to \mt{t} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1774 \mt{val} \; \mt{sql\_from\_query} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{fs} ::: \{\mt{Type}\} \to \mt{name} :: \mt{Name} \to \mt{sql\_query} \; \mt{free} \; [] \; \mt{fs} \to \mt{sql\_from\_items} \; \mt{free} \; [\mt{name} = \mt{fs}] \\
adamc@1193 1775 \mt{val} \; \mt{sql\_from\_comma} : \mt{free} ::: \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \to [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1776 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1777 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2}) \\
adamc@1193 1778 \mt{val} \; \mt{sql\_inner\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{\mt{Type}\}\} \\
adamc@1193 1779 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@1193 1780 \hspace{.1in} \Rightarrow \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs2} \\
adamc@1193 1781 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1782 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{tabs2})
adamc@786 1783 \end{array}$$
adamc@786 1784
adamc@786 1785 Besides these basic cases, outer joins are supported, which requires a type class for turning non-$\mt{option}$ columns into $\mt{option}$ columns.
adamc@786 1786 $$\begin{array}{l}
adamc@786 1787 \mt{class} \; \mt{nullify} :: \mt{Type} \to \mt{Type} \to \mt{Type} \\
adamc@786 1788 \mt{val} \; \mt{nullify\_option} : \mt{t} ::: \mt{Type} \to \mt{nullify} \; (\mt{option} \; \mt{t}) \; (\mt{option} \; \mt{t}) \\
adamc@786 1789 \mt{val} \; \mt{nullify\_prim} : \mt{t} ::: \mt{Type} \to \mt{sql\_injectable\_prim} \; \mt{t} \to \mt{nullify} \; \mt{t} \; (\mt{option} \; \mt{t})
adamc@786 1790 \end{array}$$
adamc@786 1791
adamc@786 1792 Left, right, and full outer joins can now be expressed using functions that accept records of $\mt{nullify}$ instances. Here, we give only the type for a left join as an example.
adamc@786 1793
adamc@786 1794 $$\begin{array}{l}
adamc@1193 1795 \mt{val} \; \mt{sql\_left\_join} : \mt{free} ::: \{\{\mt{Type}\}\} \to \mt{tabs1} ::: \{\{\mt{Type}\}\} \to \mt{tabs2} ::: \{\{(\mt{Type} \times \mt{Type})\}\} \\
adamc@1193 1796 \hspace{.1in} \to [\mt{free} \sim \mt{tabs1}] \Rightarrow [\mt{free} \sim \mt{tabs2}] \Rightarrow [\mt{tabs1} \sim \mt{tabs2}] \\
adamc@786 1797 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\lambda \mt{r} \Rightarrow \$(\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{nullify} \; \mt{p}.1 \; \mt{p}.2) \; \mt{r})) \; \mt{tabs2}) \\
adamc@1193 1798 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; \mt{tabs1} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \\
adamc@1193 1799 \hspace{.1in} \to \mt{sql\_exp} \; (\mt{free} \rc \mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.1)) \; \mt{tabs2}) \; [] \; [] \; \mt{bool} \\
adamc@1193 1800 \hspace{.1in} \to \mt{sql\_from\_items} \; \mt{free} \; (\mt{tabs1} \rc \mt{map} \; (\mt{map} \; (\lambda \mt{p} :: (\mt{Type} \times \mt{Type}) \Rightarrow \mt{p}.2)) \; \mt{tabs2})
adamc@786 1801 \end{array}$$
adamc@786 1802
adamc@544 1803 We wrap up the definition of query syntax with the types used in representing $\mt{ORDER} \; \mt{BY}$, $\mt{LIMIT}$, and $\mt{OFFSET}$ clauses.
adamc@544 1804 $$\begin{array}{l}
adamc@544 1805 \mt{type} \; \mt{sql\_direction} \\
adamc@544 1806 \mt{val} \; \mt{sql\_asc} : \mt{sql\_direction} \\
adamc@544 1807 \mt{val} \; \mt{sql\_desc} : \mt{sql\_direction} \\
adamc@544 1808 \\
adamc@544 1809 \mt{con} \; \mt{sql\_order\_by} :: \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \\
adamc@544 1810 \mt{val} \; \mt{sql\_order\_by\_Nil} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} :: \{\mt{Type}\} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1811 \mt{val} \; \mt{sql\_order\_by\_Cons} : \mt{tables} ::: \{\{\mt{Type}\}\} \to \mt{exps} ::: \{\mt{Type}\} \to \mt{t} ::: \mt{Type} \\
adamc@544 1812 \hspace{.1in} \to \mt{sql\_exp} \; \mt{tables} \; [] \; \mt{exps} \; \mt{t} \to \mt{sql\_direction} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \to \mt{sql\_order\_by} \; \mt{tables} \; \mt{exps} \\
adamc@544 1813 \\
adamc@544 1814 \mt{type} \; \mt{sql\_limit} \\
adamc@544 1815 \mt{val} \; \mt{sql\_no\_limit} : \mt{sql\_limit} \\
adamc@544 1816 \mt{val} \; \mt{sql\_limit} : \mt{int} \to \mt{sql\_limit} \\
adamc@544 1817 \\
adamc@544 1818 \mt{type} \; \mt{sql\_offset} \\
adamc@544 1819 \mt{val} \; \mt{sql\_no\_offset} : \mt{sql\_offset} \\
adamc@544 1820 \mt{val} \; \mt{sql\_offset} : \mt{int} \to \mt{sql\_offset}
adamc@544 1821 \end{array}$$
adamc@544 1822
adamc@545 1823
adamc@545 1824 \subsubsection{DML}
adamc@545 1825
adamc@545 1826 The Ur/Web library also includes an embedding of a fragment of SQL's DML, the Data Manipulation Language, for modifying database tables. Any piece of DML may be executed in a transaction.
adamc@545 1827
adamc@545 1828 $$\begin{array}{l}
adamc@545 1829 \mt{type} \; \mt{dml} \\
adamc@545 1830 \mt{val} \; \mt{dml} : \mt{dml} \to \mt{transaction} \; \mt{unit}
adamc@545 1831 \end{array}$$
adamc@545 1832
adam@1297 1833 The function $\mt{Basis.dml}$ will trigger a fatal application error if the command fails, for instance, because a data integrity constraint is violated. An alternate function returns an error message as a string instead.
adam@1297 1834
adam@1297 1835 $$\begin{array}{l}
adam@1297 1836 \mt{val} \; \mt{tryDml} : \mt{dml} \to \mt{transaction} \; (\mt{option} \; \mt{string})
adam@1297 1837 \end{array}$$
adam@1297 1838
adamc@545 1839 Properly-typed records may be used to form $\mt{INSERT}$ commands.
adamc@545 1840 $$\begin{array}{l}
adamc@545 1841 \mt{val} \; \mt{insert} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \\
adamc@658 1842 \hspace{.1in} \to \$(\mt{map} \; (\mt{sql\_exp} \; [] \; [] \; []) \; \mt{fields}) \to \mt{dml}
adamc@545 1843 \end{array}$$
adamc@545 1844
adamc@545 1845 An $\mt{UPDATE}$ command is formed from a choice of which table fields to leave alone and which to change, along with an expression to use to compute the new value of each changed field and a $\mt{WHERE}$ clause.
adamc@545 1846 $$\begin{array}{l}
adam@1380 1847 \mt{val} \; \mt{update} : \mt{unchanged} ::: \{\mt{Type}\} \to \mt{changed} :: \{\mt{Type}\} \to [\mt{changed} \sim \mt{unchanged}] \\
adamc@658 1848 \hspace{.1in} \Rightarrow \$(\mt{map} \; (\mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; []) \; \mt{changed}) \\
adamc@545 1849 \hspace{.1in} \to \mt{sql\_table} \; (\mt{changed} \rc \mt{unchanged}) \to \mt{sql\_exp} \; [\mt{T} = \mt{changed} \rc \mt{unchanged}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1850 \end{array}$$
adamc@545 1851
adamc@545 1852 A $\mt{DELETE}$ command is formed from a table and a $\mt{WHERE}$ clause.
adamc@545 1853 $$\begin{array}{l}
adamc@545 1854 \mt{val} \; \mt{delete} : \mt{fields} ::: \{\mt{Type}\} \to \mt{sql\_table} \; \mt{fields} \to \mt{sql\_exp} \; [\mt{T} = \mt{fields}] \; [] \; [] \; \mt{bool} \to \mt{dml}
adamc@545 1855 \end{array}$$
adamc@545 1856
adamc@546 1857 \subsubsection{Sequences}
adamc@546 1858
adamc@546 1859 SQL sequences are counters with concurrency control, often used to assign unique IDs. Ur/Web supports them via a simple interface. The only way to create a sequence is with the $\mt{sequence}$ declaration form.
adamc@546 1860
adamc@546 1861 $$\begin{array}{l}
adamc@546 1862 \mt{type} \; \mt{sql\_sequence} \\
adamc@1085 1863 \mt{val} \; \mt{nextval} : \mt{sql\_sequence} \to \mt{transaction} \; \mt{int} \\
adamc@1085 1864 \mt{val} \; \mt{setval} : \mt{sql\_sequence} \to \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@546 1865 \end{array}$$
adamc@546 1866
adamc@546 1867
adamc@547 1868 \subsection{XML}
adamc@547 1869
adam@1333 1870 Ur/Web's library contains an encoding of XML syntax and semantic constraints. We make no effort to follow the standards governing XML schemas. Rather, XML fragments are viewed more as values of ML datatypes, and we only track which tags are allowed inside which other tags. The Ur/Web standard library encodes a very loose version of XHTML, where it is very easy to produce documents which are invalid XHTML, but which still display properly in all major browsers. The main purposes of the invariants that are enforced are first, to provide some documentation about the places where it would make sense to insert XML fragments; and second, to rule out code injection attacks and other abstraction violations related to HTML syntax.
adamc@547 1871
adam@1345 1872 The basic XML type family has arguments respectively indicating the \emph{context} of a fragment, the fields that the fragment expects to be bound on entry (and their types), and the fields that the fragment will bind (and their types). Contexts are a record-based ``poor man's subtyping'' encoding, with each possible set of valid tags corresponding to a different context record. For instance, the context for the \texttt{<td>} tag is $[\mt{Body}, \mt{Tr}]$, to indicate a kind of nesting inside \texttt{<body>} and \texttt{<tr>}. Contexts are maintained in a somewhat ad-hoc way; the only definitive reference for their meanings is the types of the tag values in \texttt{basis.urs}. The arguments dealing with field binding are only relevant to HTML forms.
adamc@547 1873 $$\begin{array}{l}
adamc@547 1874 \mt{con} \; \mt{xml} :: \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1875 \end{array}$$
adamc@547 1876
adamc@547 1877 We also have a type family of XML tags, indexed respectively by the record of optional attributes accepted by the tag, the context in which the tag may be placed, the context required of children of the tag, which form fields the tag uses, and which fields the tag defines.
adamc@547 1878 $$\begin{array}{l}
adamc@547 1879 \mt{con} \; \mt{tag} :: \{\mt{Type}\} \to \{\mt{Unit}\} \to \{\mt{Unit}\} \to \{\mt{Type}\} \to \{\mt{Type}\} \to \mt{Type}
adamc@547 1880 \end{array}$$
adamc@547 1881
adamc@547 1882 Literal text may be injected into XML as ``CDATA.''
adamc@547 1883 $$\begin{array}{l}
adamc@547 1884 \mt{val} \; \mt{cdata} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{string} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adamc@547 1885 \end{array}$$
adamc@547 1886
adam@1358 1887 There is also a function to insert the literal value of a character. Since Ur/Web uses the UTF-8 text encoding, the $\mt{cdata}$ function is only sufficient to encode characters with ASCII codes below 128. Higher codes have alternate meanings in UTF-8 than in usual ASCII, so this alternate function should be used with them.
adam@1358 1888 $$\begin{array}{l}
adam@1358 1889 \mt{val} \; \mt{cdataChar} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use} ::: \{\mt{Type}\} \to \mt{char} \to \mt{xml} \; \mt{ctx} \; \mt{use} \; []
adam@1358 1890 \end{array}$$
adam@1358 1891
adamc@547 1892 There is a function for producing an XML tree with a particular tag at its root.
adamc@547 1893 $$\begin{array}{l}
adamc@547 1894 \mt{val} \; \mt{tag} : \mt{attrsGiven} ::: \{\mt{Type}\} \to \mt{attrsAbsent} ::: \{\mt{Type}\} \to \mt{ctxOuter} ::: \{\mt{Unit}\} \to \mt{ctxInner} ::: \{\mt{Unit}\} \\
adamc@547 1895 \hspace{.1in} \to \mt{useOuter} ::: \{\mt{Type}\} \to \mt{useInner} ::: \{\mt{Type}\} \to \mt{bindOuter} ::: \{\mt{Type}\} \to \mt{bindInner} ::: \{\mt{Type}\} \\
adam@1380 1896 \hspace{.1in} \to [\mt{attrsGiven} \sim \mt{attrsAbsent}] \Rightarrow [\mt{useOuter} \sim \mt{useInner}] \Rightarrow [\mt{bindOuter} \sim \mt{bindInner}] \\
adamc@787 1897 \hspace{.1in} \Rightarrow \mt{option} \; \mt{css\_class} \\
adamc@787 1898 \hspace{.1in} \to \$\mt{attrsGiven} \\
adamc@547 1899 \hspace{.1in} \to \mt{tag} \; (\mt{attrsGiven} \rc \mt{attrsAbsent}) \; \mt{ctxOuter} \; \mt{ctxInner} \; \mt{useOuter} \; \mt{bindOuter} \\
adamc@547 1900 \hspace{.1in} \to \mt{xml} \; \mt{ctxInner} \; \mt{useInner} \; \mt{bindInner} \to \mt{xml} \; \mt{ctxOuter} \; (\mt{useOuter} \rc \mt{useInner}) \; (\mt{bindOuter} \rc \mt{bindInner})
adamc@547 1901 \end{array}$$
adam@1297 1902 Note that any tag may be assigned a CSS class. This is the sole way of making use of the values produced by $\mt{style}$ declarations. Ur/Web itself doesn't deal with the syntax or semantics of style sheets; they can be linked via URLs with \texttt{link} tags. However, Ur/Web does make it easy to calculate upper bounds on usage of CSS classes through program analysis. The function $\mt{Basis.classes}$ can be used to specify a list of CSS classes for a single tag.
adamc@547 1903
adamc@547 1904 Two XML fragments may be concatenated.
adamc@547 1905 $$\begin{array}{l}
adamc@547 1906 \mt{val} \; \mt{join} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{bind_1} ::: \{\mt{Type}\} \to \mt{bind_2} ::: \{\mt{Type}\} \\
adam@1380 1907 \hspace{.1in} \to [\mt{use_1} \sim \mt{bind_1}] \Rightarrow [\mt{bind_1} \sim \mt{bind_2}] \\
adamc@547 1908 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind_1} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{bind_1}) \; \mt{bind_2} \to \mt{xml} \; \mt{ctx} \; \mt{use_1} \; (\mt{bind_1} \rc \mt{bind_2})
adamc@547 1909 \end{array}$$
adamc@547 1910
adamc@547 1911 Finally, any XML fragment may be updated to ``claim'' to use more form fields than it does.
adamc@547 1912 $$\begin{array}{l}
adam@1380 1913 \mt{val} \; \mt{useMore} : \mt{ctx} ::: \{\mt{Unit}\} \to \mt{use_1} ::: \{\mt{Type}\} \to \mt{use_2} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to [\mt{use_1} \sim \mt{use_2}] \\
adamc@547 1914 \hspace{.1in} \Rightarrow \mt{xml} \; \mt{ctx} \; \mt{use_1} \; \mt{bind} \to \mt{xml} \; \mt{ctx} \; (\mt{use_1} \rc \mt{use_2}) \; \mt{bind}
adamc@547 1915 \end{array}$$
adamc@547 1916
adam@1344 1917 We will not list here the different HTML tags and related functions from the standard library. They should be easy enough to understand from the code in \texttt{basis.urs}. The set of tags in the library is not yet claimed to be complete for HTML standards. Also note that there is currently no way for the programmer to add his own tags. It \emph{is} possible to add new tags directly to \texttt{basis.urs}, but this should only be done as a prelude to suggesting a patch to the main distribution.
adamc@547 1918
adamc@547 1919 One last useful function is for aborting any page generation, returning some XML as an error message. This function takes the place of some uses of a general exception mechanism.
adamc@547 1920 $$\begin{array}{l}
adamc@547 1921 \mt{val} \; \mt{error} : \mt{t} ::: \mt{Type} \to \mt{xml} \; [\mt{Body}] \; [] \; [] \to \mt{t}
adamc@547 1922 \end{array}$$
adamc@547 1923
adamc@549 1924
adamc@701 1925 \subsection{Client-Side Programming}
adamc@659 1926
adamc@701 1927 Ur/Web supports running code on web browsers, via automatic compilation to JavaScript.
adamc@701 1928
adamc@701 1929 \subsubsection{The Basics}
adamc@701 1930
adam@1400 1931 All of the functions in this subsection are client-side only.
adam@1400 1932
adam@1297 1933 Clients can open alert and confirm dialog boxes, in the usual annoying JavaScript way.
adamc@701 1934 $$\begin{array}{l}
adam@1297 1935 \mt{val} \; \mt{alert} : \mt{string} \to \mt{transaction} \; \mt{unit} \\
adam@1297 1936 \mt{val} \; \mt{confirm} : \mt{string} \to \mt{transaction} \; \mt{bool}
adamc@701 1937 \end{array}$$
adamc@701 1938
adamc@701 1939 Any transaction may be run in a new thread with the $\mt{spawn}$ function.
adamc@701 1940 $$\begin{array}{l}
adamc@701 1941 \mt{val} \; \mt{spawn} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit}
adamc@701 1942 \end{array}$$
adamc@701 1943
adamc@701 1944 The current thread can be paused for at least a specified number of milliseconds.
adamc@701 1945 $$\begin{array}{l}
adamc@701 1946 \mt{val} \; \mt{sleep} : \mt{int} \to \mt{transaction} \; \mt{unit}
adamc@701 1947 \end{array}$$
adamc@701 1948
adamc@787 1949 A few functions are available to registers callbacks for particular error events. Respectively, they are triggered on calls to $\mt{error}$, uncaught JavaScript exceptions, failure of remote procedure calls, the severance of the connection serving asynchronous messages, or the occurrence of some other error with that connection. If no handlers are registered for a kind of error, then occurrences of that error are ignored silently.
adamc@787 1950 $$\begin{array}{l}
adamc@787 1951 \mt{val} \; \mt{onError} : (\mt{xbody} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1952 \mt{val} \; \mt{onFail} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit} \\
adamc@787 1953 \mt{val} \; \mt{onConnectFail} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1954 \mt{val} \; \mt{onDisconnect} : \mt{transaction} \; \mt{unit} \to \mt{transaction} \; \mt{unit} \\
adamc@787 1955 \mt{val} \; \mt{onServerError} : (\mt{string} \to \mt{transaction} \; \mt{unit}) \to \mt{transaction} \; \mt{unit}
adamc@787 1956 \end{array}$$
adamc@787 1957
adamc@701 1958 \subsubsection{Functional-Reactive Page Generation}
adamc@701 1959
adamc@701 1960 Most approaches to ``AJAX''-style coding involve imperative manipulation of the DOM tree representing an HTML document's structure. Ur/Web follows the \emph{functional-reactive} approach instead. Programs may allocate mutable \emph{sources} of arbitrary types, and an HTML page is effectively a pure function over the latest values of the sources. The page is not mutated directly, but rather it changes automatically as the sources are mutated.
adamc@659 1961
adam@1403 1962 More operationally, you can think of a source as a mutable cell with facilities for subscription to change notifications. That level of detail is hidden behind a monadic facility to be described below. First, there are three primitive operations for working with sources just as if they were ML \cd{ref} cells, corresponding to ML's \cd{ref}, \cd{:=}, and \cd{!} operations.
adam@1403 1963
adamc@659 1964 $$\begin{array}{l}
adamc@659 1965 \mt{con} \; \mt{source} :: \mt{Type} \to \mt{Type} \\
adamc@659 1966 \mt{val} \; \mt{source} : \mt{t} ::: \mt{Type} \to \mt{t} \to \mt{transaction} \; (\mt{source} \; \mt{t}) \\
adamc@659 1967 \mt{val} \; \mt{set} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@659 1968 \mt{val} \; \mt{get} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@659 1969 \end{array}$$
adamc@659 1970
adam@1400 1971 Only source creation and setting are supported server-side, as a convenience to help in setting up a page, where you may wish to allocate many sources that will be referenced through the page. All server-side storage of values inside sources uses string serializations of values, while client-side storage uses normal JavaScript values.
adam@1400 1972
adam@1403 1973 Pure functions over arbitrary numbers of sources are represented in a monad of \emph{signals}, which may only be used in client-side code. This is presented to the programmer in the form of a monad $\mt{signal}$, each of whose values represents (conceptually) some pure function over all sources that may be allocated in the course of program execution. A monad operation $\mt{signal}$ denotes the identity function over a particular source. By using $\mt{signal}$ on a source, you implicitly subscribe to change notifications for that source. That is, your signal will automatically be recomputed as that source changes. The usual monad operators make it possible to build up complex signals that depend on multiple sources; automatic updating upon source-value changes still happens automatically.
adamc@659 1974
adamc@659 1975 $$\begin{array}{l}
adamc@659 1976 \mt{con} \; \mt{signal} :: \mt{Type} \to \mt{Type} \\
adamc@659 1977 \mt{val} \; \mt{signal\_monad} : \mt{monad} \; \mt{signal} \\
adamc@659 1978 \mt{val} \; \mt{signal} : \mt{t} ::: \mt{Type} \to \mt{source} \; \mt{t} \to \mt{signal} \; \mt{t}
adamc@659 1979 \end{array}$$
adamc@659 1980
adamc@659 1981 A reactive portion of an HTML page is injected with a $\mt{dyn}$ tag, which has a signal-valued attribute $\mt{Signal}$.
adamc@659 1982
adamc@659 1983 $$\begin{array}{l}
adamc@701 1984 \mt{val} \; \mt{dyn} : \mt{use} ::: \{\mt{Type}\} \to \mt{bind} ::: \{\mt{Type}\} \to \mt{unit} \\
adamc@701 1985 \hspace{.1in} \to \mt{tag} \; [\mt{Signal} = \mt{signal} \; (\mt{xml} \; \mt{body} \; \mt{use} \; \mt{bind})] \; \mt{body} \; [] \; \mt{use} \; \mt{bind}
adamc@659 1986 \end{array}$$
adamc@659 1987
adamc@701 1988 Transactions can be run on the client by including them in attributes like the $\mt{Onclick}$ attribute of $\mt{button}$, and GUI widgets like $\mt{ctextbox}$ have $\mt{Source}$ attributes that can be used to connect them to sources, so that their values can be read by code running because of, e.g., an $\mt{Onclick}$ event.
adamc@701 1989
adamc@914 1990 \subsubsection{Remote Procedure Calls}
adamc@914 1991
adamc@914 1992 Any function call may be made a client-to-server ``remote procedure call'' if the function being called needs no features that are only available to client code. To make a function call an RPC, pass that function call as the argument to $\mt{Basis.rpc}$:
adamc@914 1993
adamc@914 1994 $$\begin{array}{l}
adamc@914 1995 \mt{val} \; \mt{rpc} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@914 1996 \end{array}$$
adamc@914 1997
adamc@701 1998 \subsubsection{Asynchronous Message-Passing}
adamc@701 1999
adamc@701 2000 To support asynchronous, ``server push'' delivery of messages to clients, any client that might need to receive an asynchronous message is assigned a unique ID. These IDs may be retrieved both on the client and on the server, during execution of code related to a client.
adamc@701 2001
adamc@701 2002 $$\begin{array}{l}
adamc@701 2003 \mt{type} \; \mt{client} \\
adamc@701 2004 \mt{val} \; \mt{self} : \mt{transaction} \; \mt{client}
adamc@701 2005 \end{array}$$
adamc@701 2006
adamc@701 2007 \emph{Channels} are the means of message-passing. Each channel is created in the context of a client and belongs to that client; no other client may receive the channel's messages. Each channel type includes the type of values that may be sent over the channel. Sending and receiving are asynchronous, in the sense that a client need not be ready to receive a message right away. Rather, sent messages may queue up, waiting to be processed.
adamc@701 2008
adamc@701 2009 $$\begin{array}{l}
adamc@701 2010 \mt{con} \; \mt{channel} :: \mt{Type} \to \mt{Type} \\
adamc@701 2011 \mt{val} \; \mt{channel} : \mt{t} ::: \mt{Type} \to \mt{transaction} \; (\mt{channel} \; \mt{t}) \\
adamc@701 2012 \mt{val} \; \mt{send} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{t} \to \mt{transaction} \; \mt{unit} \\
adamc@701 2013 \mt{val} \; \mt{recv} : \mt{t} ::: \mt{Type} \to \mt{channel} \; \mt{t} \to \mt{transaction} \; \mt{t}
adamc@701 2014 \end{array}$$
adamc@701 2015
adamc@701 2016 The $\mt{channel}$ and $\mt{send}$ operations may only be executed on the server, and $\mt{recv}$ may only be executed on a client. Neither clients nor channels may be passed as arguments from clients to server-side functions, so persistent channels can only be maintained by storing them in the database and looking them up using the current client ID or some application-specific value as a key.
adamc@701 2017
adamc@701 2018 Clients and channels live only as long as the web browser page views that they are associated with. When a user surfs away, his client and its channels will be garbage-collected, after that user is not heard from for the timeout period. Garbage collection deletes any database row that contains a client or channel directly. Any reference to one of these types inside an $\mt{option}$ is set to $\mt{None}$ instead. Both kinds of handling have the flavor of weak pointers, and that is a useful way to think about clients and channels in the database.
adamc@701 2019
adamc@659 2020
adamc@549 2021 \section{Ur/Web Syntax Extensions}
adamc@549 2022
adamc@549 2023 Ur/Web features some syntactic shorthands for building values using the functions from the last section. This section sketches the grammar of those extensions. We write spans of syntax inside brackets to indicate that they are optional.
adamc@549 2024
adamc@549 2025 \subsection{SQL}
adamc@549 2026
adamc@786 2027 \subsubsection{\label{tables}Table Declarations}
adamc@786 2028
adamc@788 2029 $\mt{table}$ declarations may include constraints, via these grammar rules.
adamc@788 2030 $$\begin{array}{rrcll}
adamc@788 2031 \textrm{Declarations} & d &::=& \mt{table} \; x : c \; [pk[,]] \; cts \\
adamc@788 2032 \textrm{Primary key constraints} & pk &::=& \mt{PRIMARY} \; \mt{KEY} \; K \\
adamc@788 2033 \textrm{Keys} & K &::=& f \mid (f, (f,)^+) \\
adamc@788 2034 \textrm{Constraint sets} & cts &::=& \mt{CONSTRAINT} f \; ct \mid cts, cts \mid \{\{e\}\} \\
adamc@788 2035 \textrm{Constraints} & ct &::=& \mt{UNIQUE} \; K \mid \mt{CHECK} \; E \\
adamc@788 2036 &&& \mid \mt{FOREIGN} \; \mt{KEY} \; K \; \mt{REFERENCES} \; F \; (K) \; [\mt{ON} \; \mt{DELETE} \; pr] \; [\mt{ON} \; \mt{UPDATE} \; pr] \\
adamc@788 2037 \textrm{Foreign tables} & F &::=& x \mid \{\{e\}\} \\
adamc@788 2038 \textrm{Propagation modes} & pr &::=& \mt{NO} \; \mt{ACTION} \mid \mt{RESTRICT} \mid \mt{CASCADE} \mid \mt{SET} \; \mt{NULL}
adamc@788 2039 \end{array}$$
adamc@788 2040
adamc@788 2041 A signature item $\mt{table} \; \mt{x} : \mt{c}$ is actually elaborated into two signature items: $\mt{con} \; \mt{x\_hidden\_constraints} :: \{\{\mt{Unit}\}\}$ and $\mt{val} \; \mt{x} : \mt{sql\_table} \; \mt{c} \; \mt{x\_hidden\_constraints}$. This is appropriate for common cases where client code doesn't care which keys a table has. It's also possible to include constraints after a $\mt{table}$ signature item, with the same syntax as for $\mt{table}$ declarations. This may look like dependent typing, but it's just a convenience. The constraints are type-checked to determine a constructor $u$ to include in $\mt{val} \; \mt{x} : \mt{sql\_table} \; \mt{c} \; (u \rc \mt{x\_hidden\_constraints})$, and then the expressions are thrown away. Nonetheless, it can be useful for documentation purposes to include table constraint details in signatures. Note that the automatic generation of $\mt{x\_hidden\_constraints}$ leads to a kind of free subtyping with respect to which constraints are defined.
adamc@788 2042
adamc@788 2043
adamc@549 2044 \subsubsection{Queries}
adamc@549 2045
adamc@550 2046 Queries $Q$ are added to the rules for expressions $e$.
adamc@550 2047
adamc@549 2048 $$\begin{array}{rrcll}
adamc@550 2049 \textrm{Queries} & Q &::=& (q \; [\mt{ORDER} \; \mt{BY} \; (E \; [o],)^+] \; [\mt{LIMIT} \; N] \; [\mt{OFFSET} \; N]) \\
adamc@1085 2050 \textrm{Pre-queries} & q &::=& \mt{SELECT} \; [\mt{DISTINCT}] \; P \; \mt{FROM} \; F,^+ \; [\mt{WHERE} \; E] \; [\mt{GROUP} \; \mt{BY} \; p,^+] \; [\mt{HAVING} \; E] \\
adamc@1085 2051 &&& \mid q \; R \; q \mid \{\{\{e\}\}\} \\
adamc@549 2052 \textrm{Relational operators} & R &::=& \mt{UNION} \mid \mt{INTERSECT} \mid \mt{EXCEPT}
adamc@549 2053 \end{array}$$
adamc@549 2054
adamc@549 2055 $$\begin{array}{rrcll}
adamc@549 2056 \textrm{Projections} & P &::=& \ast & \textrm{all columns} \\
adamc@549 2057 &&& p,^+ & \textrm{particular columns} \\
adamc@549 2058 \textrm{Pre-projections} & p &::=& t.f & \textrm{one column from a table} \\
adamc@558 2059 &&& t.\{\{c\}\} & \textrm{a record of columns from a table (of kind $\{\mt{Type}\}$)} \\
adamc@1194 2060 &&& E \; [\mt{AS} \; f] & \textrm{expression column} \\
adamc@549 2061 \textrm{Table names} & t &::=& x & \textrm{constant table name (automatically capitalized)} \\
adamc@549 2062 &&& X & \textrm{constant table name} \\
adamc@549 2063 &&& \{\{c\}\} & \textrm{computed table name (of kind $\mt{Name}$)} \\
adamc@549 2064 \textrm{Column names} & f &::=& X & \textrm{constant column name} \\
adamc@549 2065 &&& \{c\} & \textrm{computed column name (of kind $\mt{Name}$)} \\
adamc@549 2066 \textrm{Tables} & T &::=& x & \textrm{table variable, named locally by its own capitalization} \\
adamc@549 2067 &&& x \; \mt{AS} \; t & \textrm{table variable, with local name} \\
adamc@549 2068 &&& \{\{e\}\} \; \mt{AS} \; t & \textrm{computed table expression, with local name} \\
adamc@1085 2069 \textrm{$\mt{FROM}$ items} & F &::=& T \mid \{\{e\}\} \mid F \; J \; \mt{JOIN} \; F \; \mt{ON} \; E \\
adamc@1085 2070 &&& \mid F \; \mt{CROSS} \; \mt{JOIN} \ F \\
adamc@1193 2071 &&& \mid (Q) \; \mt{AS} \; t \\
adamc@1085 2072 \textrm{Joins} & J &::=& [\mt{INNER}] \\
adamc@1085 2073 &&& \mid [\mt{LEFT} \mid \mt{RIGHT} \mid \mt{FULL}] \; [\mt{OUTER}] \\
adamc@549 2074 \textrm{SQL expressions} & E &::=& p & \textrm{column references} \\
adamc@549 2075 &&& X & \textrm{named expression references} \\
adam@1490 2076 &&& \{[e]\} & \textrm{injected native Ur expressions} \\
adamc@549 2077 &&& \{e\} & \textrm{computed expressions, probably using $\mt{sql\_exp}$ directly} \\
adamc@549 2078 &&& \mt{TRUE} \mid \mt{FALSE} & \textrm{boolean constants} \\
adamc@549 2079 &&& \ell & \textrm{primitive type literals} \\
adamc@549 2080 &&& \mt{NULL} & \textrm{null value (injection of $\mt{None}$)} \\
adamc@549 2081 &&& E \; \mt{IS} \; \mt{NULL} & \textrm{nullness test} \\
adamc@549 2082 &&& n & \textrm{nullary operators} \\
adamc@549 2083 &&& u \; E & \textrm{unary operators} \\
adamc@549 2084 &&& E \; b \; E & \textrm{binary operators} \\
adamc@549 2085 &&& \mt{COUNT}(\ast) & \textrm{count number of rows} \\
adamc@549 2086 &&& a(E) & \textrm{other aggregate function} \\
adamc@1193 2087 &&& (Q) & \textrm{subquery (must return a single expression column)} \\
adamc@549 2088 &&& (E) & \textrm{explicit precedence} \\
adamc@549 2089 \textrm{Nullary operators} & n &::=& \mt{CURRENT\_TIMESTAMP} \\
adamc@549 2090 \textrm{Unary operators} & u &::=& \mt{NOT} \\
adamc@549 2091 \textrm{Binary operators} & b &::=& \mt{AND} \mid \mt{OR} \mid \neq \mid < \mid \leq \mid > \mid \geq \\
adamc@1188 2092 \textrm{Aggregate functions} & a &::=& \mt{COUNT} \mid \mt{AVG} \mid \mt{SUM} \mid \mt{MIN} \mid \mt{MAX} \\
adamc@550 2093 \textrm{Directions} & o &::=& \mt{ASC} \mid \mt{DESC} \\
adamc@549 2094 \textrm{SQL integer} & N &::=& n \mid \{e\} \\
adamc@549 2095 \end{array}$$
adamc@549 2096
adamc@1085 2097 Additionally, an SQL expression may be inserted into normal Ur code with the syntax $(\mt{SQL} \; E)$ or $(\mt{WHERE} \; E)$. Similar shorthands exist for other nonterminals, with the prefix $\mt{FROM}$ for $\mt{FROM}$ items and $\mt{SELECT1}$ for pre-queries.
adamc@549 2098
adamc@1194 2099 Unnamed expression columns in $\mt{SELECT}$ clauses are assigned consecutive natural numbers, starting with 1.
adamc@1194 2100
adamc@550 2101 \subsubsection{DML}
adamc@550 2102
adamc@550 2103 DML commands $D$ are added to the rules for expressions $e$.
adamc@550 2104
adamc@550 2105 $$\begin{array}{rrcll}
adamc@550 2106 \textrm{Commands} & D &::=& (\mt{INSERT} \; \mt{INTO} \; T^E \; (f,^+) \; \mt{VALUES} \; (E,^+)) \\
adamc@550 2107 &&& (\mt{UPDATE} \; T^E \; \mt{SET} \; (f = E,)^+ \; \mt{WHERE} \; E) \\
adamc@550 2108 &&& (\mt{DELETE} \; \mt{FROM} \; T^E \; \mt{WHERE} \; E) \\
adamc@550 2109 \textrm{Table expressions} & T^E &::=& x \mid \{\{e\}\}
adamc@550 2110 \end{array}$$
adamc@550 2111
adamc@550 2112 Inside $\mt{UPDATE}$ and $\mt{DELETE}$ commands, lone variables $X$ are interpreted as references to columns of the implicit table $\mt{T}$, rather than to named expressions.
adamc@549 2113
adamc@551 2114 \subsection{XML}
adamc@551 2115
adamc@551 2116 XML fragments $L$ are added to the rules for expressions $e$.
adamc@551 2117
adamc@551 2118 $$\begin{array}{rrcll}
adamc@551 2119 \textrm{XML fragments} & L &::=& \texttt{<xml/>} \mid \texttt{<xml>}l^*\texttt{</xml>} \\
adamc@551 2120 \textrm{XML pieces} & l &::=& \textrm{text} & \textrm{cdata} \\
adamc@551 2121 &&& \texttt{<}g\texttt{/>} & \textrm{tag with no children} \\
adamc@551 2122 &&& \texttt{<}g\texttt{>}l^*\texttt{</}x\texttt{>} & \textrm{tag with children} \\
adamc@559 2123 &&& \{e\} & \textrm{computed XML fragment} \\
adamc@559 2124 &&& \{[e]\} & \textrm{injection of an Ur expression, via the $\mt{Top}.\mt{txt}$ function} \\
adamc@551 2125 \textrm{Tag} & g &::=& h \; (x = v)^* \\
adamc@551 2126 \textrm{Tag head} & h &::=& x & \textrm{tag name} \\
adamc@551 2127 &&& h\{c\} & \textrm{constructor parameter} \\
adamc@551 2128 \textrm{Attribute value} & v &::=& \ell & \textrm{literal value} \\
adamc@551 2129 &&& \{e\} & \textrm{computed value} \\
adamc@551 2130 \end{array}$$
adamc@551 2131
adamc@552 2132
adamc@1198 2133 \section{\label{structure}The Structure of Web Applications}
adamc@553 2134
adamc@1127 2135 A web application is built from a series of modules, with one module, the last one appearing in the \texttt{.urp} file, designated as the main module. The signature of the main module determines the URL entry points to the application. Such an entry point should have type $\mt{t1} \to \ldots \to \mt{tn} \to \mt{transaction} \; \mt{page}$, for any integer $n \geq 0$, where $\mt{page}$ is a type synonym for top-level HTML pages, defined in $\mt{Basis}$. If such a function is at the top level of main module $M$, with $n = 0$, it will be accessible at URI \texttt{/M/f}, and so on for more deeply-nested functions, as described in Section \ref{tag} below. Arguments to an entry-point function are deserialized from the part of the URI following \texttt{f}.
adamc@553 2136
adam@1347 2137 Normal links are accessible via HTTP \texttt{GET}, which the relevant standard says should never cause side effects. To export a page which may cause side effects, accessible only via HTTP \texttt{POST}, include one argument of the page handler of type $\mt{Basis.postBody}$. When the handler is called, this argument will receive a value that can be deconstructed into a MIME type (with $\mt{Basis.postType}$) and payload (with $\mt{Basis.postData}$). This kind of handler will only work with \texttt{POST} payloads of MIME types besides those associated with HTML forms; for these, use Ur/Web's built-in support, as described below.
adam@1347 2138
adam@1370 2139 Any normal page handler may also include arguments of type $\mt{option \; Basis.queryString}$, which will be handled specially. Rather than being deserialized from the current URI, such an argument is passed the whole query string that the handler received. The string may be analyzed by calling $\mt{Basis.show}$ on it. A handler of this kind may be passed as an argument to $\mt{Basis.effectfulUrl}$ to generate a URL to a page that may be used as a ``callback'' by an external service, such that the handler is allowed to cause side effects.
adam@1370 2140
adamc@553 2141 When the standalone web server receives a request for a known page, it calls the function for that page, ``running'' the resulting transaction to produce the page to return to the client. Pages link to other pages with the \texttt{link} attribute of the \texttt{a} HTML tag. A link has type $\mt{transaction} \; \mt{page}$, and the semantics of a link are that this transaction should be run to compute the result page, when the link is followed. Link targets are assigned URL names in the same way as top-level entry points.
adamc@553 2142
adamc@553 2143 HTML forms are handled in a similar way. The $\mt{action}$ attribute of a $\mt{submit}$ form tag takes a value of type $\$\mt{use} \to \mt{transaction} \; \mt{page}$, where $\mt{use}$ is a kind-$\{\mt{Type}\}$ record of the form fields used by this action handler. Action handlers are assigned URL patterns in the same way as above.
adamc@553 2144
adamc@558 2145 For both links and actions, direct arguments and local variables mentioned implicitly via closures are automatically included in serialized form in URLs, in the order in which they appear in the source code.
adamc@553 2146
adamc@660 2147 Ur/Web programs generally mix server- and client-side code in a fairly transparent way. The one important restriction is that mixed client-server code must encapsulate all server-side pieces within named functions. This is because execution of such pieces will be implemented by explicit calls to the remote web server, and it is useful to get the programmer's help in designing the interface to be used. For example, this makes it easier to allow a client running an old version of an application to continue interacting with a server that has been upgraded to a new version, if the programmer took care to keep the interfaces of all of the old remote calls the same. The functions implementing these services are assigned names in the same way as normal web entry points, by using module structure.
adamc@660 2148
adamc@789 2149 \medskip
adamc@789 2150
adam@1347 2151 The HTTP standard suggests that GET requests only be used in ways that generate no side effects. Side effecting operations should use POST requests instead. The Ur/Web compiler enforces this rule strictly, via a simple conservative program analysis. Any page that may have a side effect must be accessed through a form, all of which use POST requests, or via a direct call to a page handler with some argument of type $\mt{Basis.postBody}$. A page is judged to have a side effect if its code depends syntactically on any of the side-effecting, server-side FFI functions. Links, forms, and most client-side event handlers are not followed during this syntactic traversal, but \texttt{<body onload=\{...\}>} handlers \emph{are} examined, since they run right away and could just as well be considered parts of main page handlers.
adamc@789 2152
adamc@789 2153 Ur/Web includes a kind of automatic protection against cross site request forgery attacks. Whenever any page execution can have side effects and can also read at least one cookie value, all cookie values must be signed cryptographically, to ensure that the user has come to the current page by submitting a form on a real page generated by the proper server. Signing and signature checking are inserted automatically by the compiler. This prevents attacks like phishing schemes where users are directed to counterfeit pages with forms that submit to your application, where a user's cookies might be submitted without his knowledge, causing some undesired side effect.
adamc@789 2154
adam@1348 2155 \subsection{Tasks}
adam@1348 2156
adam@1348 2157 In many web applications, it's useful to run code at points other than requests from browsers. Ur/Web's \emph{task} mechanism facilitates this. A type family of \emph{task kinds} is in the standard library:
adam@1348 2158
adam@1348 2159 $$\begin{array}{l}
adam@1348 2160 \mt{con} \; \mt{task\_kind} :: \mt{Type} \to \mt{Type} \\
adam@1348 2161 \mt{val} \; \mt{initialize} : \mt{task\_kind} \; \mt{unit} \\
adam@1349 2162 \mt{val} \; \mt{clientLeaves} : \mt{task\_kind} \; \mt{client} \\
adam@1349 2163 \mt{val} \; \mt{periodic} : \mt{int} \to \mt{task\_kind} \; \mt{unit}
adam@1348 2164 \end{array}$$
adam@1348 2165
adam@1348 2166 A task kind names a particular extension point of generated applications, where the type parameter of a task kind describes which extra input data is available at that extension point. Add task code with the special declaration form $\mt{task} \; e_1 = e_2$, where $e_1$ is a task kind with data $\tau$, and $e_2$ is a function from $\tau$ to $\mt{transaction} \; \mt{unit}$.
adam@1348 2167
adam@1348 2168 The currently supported task kinds are:
adam@1348 2169 \begin{itemize}
adam@1349 2170 \item $\mt{initialize}$: Code that is run when the application starts up.
adam@1348 2171 \item $\mt{clientLeaves}$: Code that is run for each client that the runtime system decides has surfed away. When a request that generates a new client handle is aborted, that handle will still eventually be passed to $\mt{clientLeaves}$ task code, even though the corresponding browser was never informed of the client handle's existence. In other words, in general, $\mt{clientLeaves}$ handlers will be called more times than there are actual clients.
adam@1349 2172 \item $\mt{periodic} \; n$: Code that is run when the application starts up and then every $n$ seconds thereafter.
adam@1348 2173 \end{itemize}
adam@1348 2174
adamc@553 2175
adamc@897 2176 \section{The Foreign Function Interface}
adamc@897 2177
adamc@897 2178 It is possible to call your own C and JavaScript code from Ur/Web applications, via the foreign function interface (FFI). The starting point for a new binding is a \texttt{.urs} signature file that presents your external library as a single Ur/Web module (with no nested modules). Compilation conventions map the types and values that you use into C and/or JavaScript types and values.
adamc@897 2179
adamc@897 2180 It is most convenient to encapsulate an FFI binding with a new \texttt{.urp} file, which applications can include with the \texttt{library} directive in their own \texttt{.urp} files. A number of directives are likely to show up in the library's project file.
adamc@897 2181
adamc@897 2182 \begin{itemize}
adamc@897 2183 \item \texttt{clientOnly Module.ident} registers a value as being allowed only in client-side code.
adamc@897 2184 \item \texttt{clientToServer Module.ident} declares a type as OK to marshal between clients and servers. By default, abstract FFI types are not allowed to be marshalled, since your library might be maintaining invariants that the simple serialization code doesn't check.
adamc@897 2185 \item \texttt{effectful Module.ident} registers a function that can have side effects. It is important to remember to use this directive for each such function, or else the optimizer might change program semantics.
adamc@897 2186 \item \texttt{ffi FILE.urs} names the file giving your library's signature. You can include multiple such files in a single \texttt{.urp} file, and each file \texttt{mod.urp} defines an FFI module \texttt{Mod}.
adamc@1099 2187 \item \texttt{include FILE} requests inclusion of a C header file.
adamc@897 2188 \item \texttt{jsFunc Module.ident=name} gives a mapping from an Ur name for a value to a JavaScript name.
adamc@897 2189 \item \texttt{link FILE} requests that \texttt{FILE} be linked into applications. It should be a C object or library archive file, and you are responsible for generating it with your own build process.
adamc@897 2190 \item \texttt{script URL} requests inclusion of a JavaScript source file within application HTML.
adamc@897 2191 \item \texttt{serverOnly Module.ident} registers a value as being allowed only in server-side code.
adamc@897 2192 \end{itemize}
adamc@897 2193
adamc@897 2194 \subsection{Writing C FFI Code}
adamc@897 2195
adamc@897 2196 A server-side FFI type or value \texttt{Module.ident} must have a corresponding type or value definition \texttt{uw\_Module\_ident} in C code. With the current Ur/Web version, it's not generally possible to work with Ur records or complex datatypes in C code, but most other kinds of types are fair game.
adamc@897 2197
adamc@897 2198 \begin{itemize}
adamc@897 2199 \item Primitive types defined in \texttt{Basis} are themselves using the standard FFI interface, so you may refer to them like \texttt{uw\_Basis\_t}. See \texttt{include/types.h} for their definitions.
adamc@897 2200 \item Enumeration datatypes, which have only constructors that take no arguments, should be defined using C \texttt{enum}s. The type is named as for any other type identifier, and each constructor \texttt{c} gets an enumeration constant named \texttt{uw\_Module\_c}.
adamc@897 2201 \item A datatype \texttt{dt} (such as \texttt{Basis.option}) that has one non-value-carrying constructor \texttt{NC} and one value-carrying constructor \texttt{C} gets special treatment. Where \texttt{T} is the type of \texttt{C}'s argument, and where we represent \texttt{T} as \texttt{t} in C, we represent \texttt{NC} with \texttt{NULL}. The representation of \texttt{C} depends on whether we're sure that we don't need to use \texttt{NULL} to represent \texttt{t} values; this condition holds only for strings and complex datatypes. For such types, \texttt{C v} is represented with the C encoding of \texttt{v}, such that the translation of \texttt{dt} is \texttt{t}. For other types, \texttt{C v} is represented with a pointer to the C encoding of v, such that the translation of \texttt{dt} is \texttt{t*}.
adamc@897 2202 \end{itemize}
adamc@897 2203
adamc@897 2204 The C FFI version of a Ur function with type \texttt{T1 -> ... -> TN -> R} or \texttt{T1 -> ... -> TN -> transaction R} has a C prototype like \texttt{R uw\_Module\_ident(uw\_context, T1, ..., TN)}. Only functions with types of the second form may have side effects. \texttt{uw\_context} is the type of state that persists across handling a client request. Many functions that operate on contexts are prototyped in \texttt{include/urweb.h}. Most should only be used internally by the compiler. A few are useful in general FFI implementation:
adamc@897 2205 \begin{itemize}
adamc@897 2206 \item \begin{verbatim}
adamc@897 2207 void uw_error(uw_context, failure_kind, const char *fmt, ...);
adamc@897 2208 \end{verbatim}
adamc@897 2209 Abort the current request processing, giving a \texttt{printf}-style format string and arguments for generating an error message. The \texttt{failure\_kind} argument can be \texttt{FATAL}, to abort the whole execution; \texttt{BOUNDED\_RETRY}, to try processing the request again from the beginning, but failing if this happens too many times; or \texttt{UNLIMITED\_RETRY}, to repeat processing, with no cap on how many times this can recur.
adamc@897 2210
adam@1329 2211 All pointers to the context-local heap (see description below of \texttt{uw\_malloc()}) become invalid at the start and end of any execution of a main entry point function of an application. For example, if the request handler is restarted because of a \texttt{uw\_error()} call with \texttt{BOUNDED\_RETRY} or for any other reason, it is unsafe to access any local heap pointers that may have been stashed somewhere beforehand.
adam@1329 2212
adamc@897 2213 \item \begin{verbatim}
adam@1469 2214 void uw_set_error_message(uw_context, const char *fmt, ...);
adam@1469 2215 \end{verbatim}
adam@1469 2216 This simpler form of \texttt{uw\_error()} saves an error message without immediately aborting execution.
adam@1469 2217
adam@1469 2218 \item \begin{verbatim}
adamc@897 2219 void uw_push_cleanup(uw_context, void (*func)(void *), void *arg);
adamc@897 2220 void uw_pop_cleanup(uw_context);
adamc@897 2221 \end{verbatim}
adam@1329 2222 Manipulate a stack of actions that should be taken if any kind of error condition arises. Calling the ``pop'' function both removes an action from the stack and executes it. It is a bug to let a page request handler finish successfully with unpopped cleanup actions.
adam@1329 2223
adam@1329 2224 Pending cleanup actions aren't intended to have any complex relationship amongst themselves, so, upon request handler abort, pending actions are executed in first-in-first-out order.
adamc@897 2225
adamc@897 2226 \item \begin{verbatim}
adamc@897 2227 void *uw_malloc(uw_context, size_t);
adamc@897 2228 \end{verbatim}
adam@1329 2229 A version of \texttt{malloc()} that allocates memory inside a context's heap, which is managed with region allocation. Thus, there is no \texttt{uw\_free()}, but you need to be careful not to keep ad-hoc C pointers to this area of memory. In general, \texttt{uw\_malloc()}ed memory should only be used in ways compatible with the computation model of pure Ur. This means it is fine to allocate and return a value that could just as well have been built with core Ur code. In contrast, it is almost never safe to store \texttt{uw\_malloc()}ed pointers in global variables, including when the storage happens implicitly by registering a callback that would take the pointer as an argument.
adam@1329 2230
adam@1329 2231 For performance and correctness reasons, it is usually preferable to use \texttt{uw\_malloc()} instead of \texttt{malloc()}. The former manipulates a local heap that can be kept allocated across page requests, while the latter uses global data structures that may face contention during concurrent execution. However, we emphasize again that \texttt{uw\_malloc()} should never be used to implement some logic that couldn't be implemented trivially by a constant-valued expression in Ur.
adamc@897 2232
adamc@897 2233 \item \begin{verbatim}
adamc@897 2234 typedef void (*uw_callback)(void *);
adam@1328 2235 typedef void (*uw_callback_with_retry)(void *, int will_retry);
adamc@897 2236 void uw_register_transactional(uw_context, void *data, uw_callback commit,
adam@1328 2237 uw_callback rollback, uw_callback_with_retry free);
adamc@897 2238 \end{verbatim}
adam@1328 2239 All side effects in Ur/Web programs need to be compatible with transactions, such that any set of actions can be undone at any time. Thus, you should not perform actions with non-local side effects directly; instead, register handlers to be called when the current transaction is committed or rolled back. The arguments here give an arbitary piece of data to be passed to callbacks, a function to call on commit, a function to call on rollback, and a function to call afterward in either case to clean up any allocated resources. A rollback handler may be called after the associated commit handler has already been called, if some later part of the commit process fails. A free handler is told whether the runtime system expects to retry the current page request after rollback finishes.
adamc@897 2240
adamc@1085 2241 Any of the callbacks may be \texttt{NULL}. To accommodate some stubbornly non-transactional real-world actions like sending an e-mail message, Ur/Web treats \texttt{NULL} \texttt{rollback} callbacks specially. When a transaction commits, all \texttt{commit} actions that have non-\texttt{NULL} rollback actions are tried before any \texttt{commit} actions that have \texttt{NULL} rollback actions. Thus, if a single execution uses only one non-transactional action, and if that action never fails partway through its execution while still causing an observable side effect, then Ur/Web can maintain the transactional abstraction.
adamc@1085 2242
adam@1329 2243 When a request handler ends with multiple pending transactional actions, their handlers are run in a first-in-last-out stack-like order, wherever the order would otherwise be ambiguous.
adam@1329 2244
adam@1329 2245 It is not safe for any of these handlers to access a context-local heap through a pointer returned previously by \texttt{uw\_malloc()}, nor should any new calls to that function be made. Think of the context-local heap as meant for use by the Ur/Web code itself, while transactional handlers execute after the Ur/Web code has finished.
adam@1329 2246
adam@1469 2247 A handler may signal an error by calling \texttt{uw\_set\_error\_message()}, but it is not safe to call \texttt{uw\_error()} from a handler. Signaling an error in a commit handler will cause the runtime system to switch to aborting the transaction, immediately after the current commit handler returns.
adam@1469 2248
adamc@1085 2249 \item \begin{verbatim}
adamc@1085 2250 void *uw_get_global(uw_context, char *name);
adamc@1085 2251 void uw_set_global(uw_context, char *name, void *data, uw_callback free);
adamc@1085 2252 \end{verbatim}
adam@1329 2253 Different FFI-based extensions may want to associate their own pieces of data with contexts. The global interface provides a way of doing that, where each extension must come up with its own unique key. The \texttt{free} argument to \texttt{uw\_set\_global()} explains how to deallocate the saved data. It is never safe to store \texttt{uw\_malloc()}ed pointers in global variable slots.
adamc@1085 2254
adamc@897 2255 \end{itemize}
adamc@897 2256
adamc@897 2257 \subsection{Writing JavaScript FFI Code}
adamc@897 2258
adamc@897 2259 JavaScript is dynamically typed, so Ur/Web type definitions imply no JavaScript code. The JavaScript identifier for each FFI function is set with the \texttt{jsFunc} directive. Each identifier can be defined in any JavaScript file that you ask to include with the \texttt{script} directive.
adamc@897 2260
adamc@897 2261 In contrast to C FFI code, JavaScript FFI functions take no extra context argument. Their argument lists are as you would expect from their Ur types. Only functions whose ranges take the form \texttt{transaction T} should have side effects; the JavaScript ``return type'' of such a function is \texttt{T}. Here are the conventions for representing Ur values in JavaScript.
adamc@897 2262
adamc@897 2263 \begin{itemize}
adamc@897 2264 \item Integers, floats, strings, characters, and booleans are represented in the usual JavaScript way.
adamc@985 2265 \item Ur functions are represented in an unspecified way. This means that you should not rely on any details of function representation. Named FFI functions are represented as JavaScript functions with as many arguments as their Ur types specify. To call a non-FFI function \texttt{f} on argument \texttt{x}, run \texttt{execF(f, x)}.
adamc@897 2266 \item An Ur record is represented with a JavaScript record, where Ur field name \texttt{N} translates to JavaScript field name \texttt{\_N}. An exception to this rule is that the empty record is encoded as \texttt{null}.
adamc@897 2267 \item \texttt{option}-like types receive special handling similar to their handling in C. The ``\texttt{None}'' constructor is \texttt{null}, and a use of the ``\texttt{Some}'' constructor on a value \texttt{v} is either \texttt{v}, if the underlying type doesn't need to use \texttt{null}; or \texttt{\{v:v\}} otherwise.
adamc@985 2268 \item Any other datatypes represent a non-value-carrying constructor \texttt{C} as \texttt{"C"} and an application of a constructor \texttt{C} to value \texttt{v} as \texttt{\{n:"C", v:v\}}. This rule only applies to datatypes defined in FFI module signatures; the compiler is free to optimize the representations of other, non-\texttt{option}-like datatypes in arbitrary ways.
adamc@897 2269 \end{itemize}
adamc@897 2270
adamc@897 2271 It is possible to write JavaScript FFI code that interacts with the functional-reactive structure of a document, but this version of the manual doesn't cover the details.
adamc@897 2272
adamc@897 2273
adamc@552 2274 \section{Compiler Phases}
adamc@552 2275
adamc@552 2276 The Ur/Web compiler is unconventional in that it relies on a kind of \emph{heuristic compilation}. Not all valid programs will compile successfully. Informally, programs fail to compile when they are ``too higher order.'' Compiler phases do their best to eliminate different kinds of higher order-ness, but some programs just won't compile. This is a trade-off for producing very efficient executables. Compiled Ur/Web programs use native C representations and require no garbage collection.
adamc@552 2277
adamc@552 2278 In this section, we step through the main phases of compilation, noting what consequences each phase has for effective programming.
adamc@552 2279
adamc@552 2280 \subsection{Parse}
adamc@552 2281
adamc@552 2282 The compiler reads a \texttt{.urp} file, figures out which \texttt{.urs} and \texttt{.ur} files it references, and combines them all into what is conceptually a single sequence of declarations in the core language of Section \ref{core}.
adamc@552 2283
adamc@552 2284 \subsection{Elaborate}
adamc@552 2285
adamc@552 2286 This is where type inference takes place, translating programs into an explicit form with no more wildcards. This phase is the most likely source of compiler error messages.
adamc@552 2287
adam@1378 2288 Those crawling through the compiler source will also want to be aware of another compiler phase, Explify, that occurs immediately afterward. This phase just translates from an AST language that includes unification variables to a very similar language that doesn't; all variables should have been determined by the end of Elaborate, anyway. The new AST language also drops some features that are used only for static checking and that have no influence on runtime behavior, like disjointness constraints.
adam@1378 2289
adamc@552 2290 \subsection{Unnest}
adamc@552 2291
adamc@552 2292 Named local function definitions are moved to the top level, to avoid the need to generate closures.
adamc@552 2293
adamc@552 2294 \subsection{Corify}
adamc@552 2295
adamc@552 2296 Module system features are compiled away, through inlining of functor definitions at application sites. Afterward, most abstraction boundaries are broken, facilitating optimization.
adamc@552 2297
adamc@552 2298 \subsection{Especialize}
adamc@552 2299
adam@1356 2300 Functions are specialized to particular argument patterns. This is an important trick for avoiding the need to maintain any closures at runtime. Currently, specialization only happens for prefixes of a function's full list of parameters, so you may need to take care to put arguments of function types before other arguments. The optimizer will not be effective enough if you use arguments that mix functions and values that must be calculated at run-time. For instance, a tuple of a function and an integer counter would not lead to successful code generation; these should be split into separate arguments via currying.
adamc@552 2301
adamc@552 2302 \subsection{Untangle}
adamc@552 2303
adamc@552 2304 Remove unnecessary mutual recursion, splitting recursive groups into strongly-connected components.
adamc@552 2305
adamc@552 2306 \subsection{Shake}
adamc@552 2307
adamc@552 2308 Remove all definitions not needed to run the page handlers that are visible in the signature of the last module listed in the \texttt{.urp} file.
adamc@552 2309
adamc@661 2310 \subsection{Rpcify}
adamc@661 2311
adamc@661 2312 Pieces of code are determined to be client-side, server-side, neither, or both, by figuring out which standard library functions might be needed to execute them. Calls to server-side functions (e.g., $\mt{query}$) within mixed client-server code are identified and replaced with explicit remote calls. Some mixed functions may be converted to continuation-passing style to facilitate this transformation.
adamc@661 2313
adamc@661 2314 \subsection{Untangle, Shake}
adamc@661 2315
adamc@661 2316 Repeat these simplifications.
adamc@661 2317
adamc@553 2318 \subsection{\label{tag}Tag}
adamc@552 2319
adamc@552 2320 Assign a URL name to each link and form action. It is important that these links and actions are written as applications of named functions, because such names are used to generate URL patterns. A URL pattern has a name built from the full module path of the named function, followed by the function name, with all pieces separated by slashes. The path of a functor application is based on the name given to the result, rather than the path of the functor itself.
adamc@552 2321
adamc@552 2322 \subsection{Reduce}
adamc@552 2323
adamc@552 2324 Apply definitional equality rules to simplify the program as much as possible. This effectively includes inlining of every non-recursive definition.
adamc@552 2325
adamc@552 2326 \subsection{Unpoly}
adamc@552 2327
adamc@552 2328 This phase specializes polymorphic functions to the specific arguments passed to them in the program. If the program contains real polymorphic recursion, Unpoly will be insufficient to avoid later error messages about too much polymorphism.
adamc@552 2329
adamc@552 2330 \subsection{Specialize}
adamc@552 2331
adamc@558 2332 Replace uses of parameterized datatypes with versions specialized to specific parameters. As for Unpoly, this phase will not be effective enough in the presence of polymorphic recursion or other fancy uses of impredicative polymorphism.
adamc@552 2333
adamc@552 2334 \subsection{Shake}
adamc@552 2335
adamc@558 2336 Here the compiler repeats the earlier Shake phase.
adamc@552 2337
adamc@552 2338 \subsection{Monoize}
adamc@552 2339
adamc@552 2340 Programs are translated to a new intermediate language without polymorphism or non-$\mt{Type}$ constructors. Error messages may pop up here if earlier phases failed to remove such features.
adamc@552 2341
adamc@552 2342 This is the stage at which concrete names are generated for cookies, tables, and sequences. They are named following the same convention as for links and actions, based on module path information saved from earlier stages. Table and sequence names separate path elements with underscores instead of slashes, and they are prefixed by \texttt{uw\_}.
adamc@664 2343
adamc@552 2344 \subsection{MonoOpt}
adamc@552 2345
adamc@552 2346 Simple algebraic laws are applied to simplify the program, focusing especially on efficient imperative generation of HTML pages.
adamc@552 2347
adamc@552 2348 \subsection{MonoUntangle}
adamc@552 2349
adamc@552 2350 Unnecessary mutual recursion is broken up again.
adamc@552 2351
adamc@552 2352 \subsection{MonoReduce}
adamc@552 2353
adamc@552 2354 Equivalents of the definitional equality rules are applied to simplify programs, with inlining again playing a major role.
adamc@552 2355
adamc@552 2356 \subsection{MonoShake, MonoOpt}
adamc@552 2357
adamc@552 2358 Unneeded declarations are removed, and basic optimizations are repeated.
adamc@552 2359
adamc@552 2360 \subsection{Fuse}
adamc@552 2361
adamc@552 2362 The compiler tries to simplify calls to recursive functions whose results are immediately written as page output. The write action is pushed inside the function definitions to avoid allocation of intermediate results.
adamc@552 2363
adamc@552 2364 \subsection{MonoUntangle, MonoShake}
adamc@552 2365
adamc@552 2366 Fuse often creates more opportunities to remove spurious mutual recursion.
adamc@552 2367
adamc@552 2368 \subsection{Pathcheck}
adamc@552 2369
adamc@552 2370 The compiler checks that no link or action name has been used more than once.
adamc@552 2371
adamc@552 2372 \subsection{Cjrize}
adamc@552 2373
adamc@552 2374 The program is translated to what is more or less a subset of C. If any use of functions as data remains at this point, the compiler will complain.
adamc@552 2375
adamc@552 2376 \subsection{C Compilation and Linking}
adamc@552 2377
adamc@552 2378 The output of the last phase is pretty-printed as C source code and passed to GCC.
adamc@552 2379
adamc@552 2380
adamc@524 2381 \end{document}